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                # Licensed under a 3-clause BSD style license - see LICENSE  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                """Methods for correlation of light curves."""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import logging  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import numpy as np  | 
            
                            
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                from numba import jit, float64, vectorize, guvectorize  | 
            
                            
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                from mutis.lib.utils import get_grid  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                __all__ = [  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "kroedel_old",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "welsh_old",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "kroedel",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "welsh",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "nindcf",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "gen_times_rawab",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "gen_times_uniform",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    "gen_times_canopy",  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                ]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                log = logging.getLogger(__name__)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def _kroedel_old(t1, d1, t2, d2, t, dt):  | 
            
                            
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                    t1m, t2m = get_grid(t1, t2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    d1m, d2m = np.meshgrid(d1, d2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    mask = ((t - dt / 2) < (t2m - t1m)) & ((t2m - t1m) < (t + dt / 2))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    udcf = (d1m - np.mean(d1)) * (d2m - np.mean(d2)) / np.std(d1) / np.std(d2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return np.mean(udcf[mask])  | 
            
            
                                                                        
                            
            
                                    
            
            
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                View Code Duplication | 
                def kroedel_old(t1, d1, t2, d2, t, dt):  | 
            
                            
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                    """Krolik & Edelson (1988) correlation with adaptative binning.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    Old version, not using numba. Kept for debugging purposes.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    if t.size != dt.size:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        log.error("Error, t and dt not the same size") | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return False  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    if t1.size != d1.size:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        log.error("Error, t1 and d1 not the same size") | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return False  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    if t2.size != d2.size:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        log.error("Error, t2 and d2 not the same size") | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return False  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    res = np.empty(t.size)  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    for i in range(t.size):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        res[i] = _kroedel_old(t1, d1, t2, d2, t[i], dt[i])  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    return res  | 
            
            
                                                                        
                            
            
                                    
            
            
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                def _welsh_old(t1, d1, t2, d2, t, dt):  | 
            
                            
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                    t1m, t2m = get_grid(t1, t2)  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    d1m, d2m = np.meshgrid(d1, d2)  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    msk = ((t - dt / 2) < (t2m - t1m)) & ((t2m - t1m) < (t + dt / 2))  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    udcf = (  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        (d1m - np.mean(d1m[msk])) * (d2m - np.mean(d2m[msk])) / np.std(d1m[msk]) / np.std(d2m[msk])  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    )  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    return np.mean(udcf[msk])  | 
            
            
                                                                        
                            
            
                                    
            
            
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                View Code Duplication | 
                def welsh_old(t1, d1, t2, d2, t, dt):  | 
            
                            
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                    """Welsh (1999) correlation with adaptative binning.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    Old version, not using numba. Kept for debugging purposes.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    if t.size != dt.size:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        log.error("Error, t and dt not the same size") | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return False  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    if t1.size != d1.size:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        log.error("Error, t1 and d1 not the same size") | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return False  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    if t2.size != d2.size:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        log.error("Error, t2 and d2 not the same size") | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return False  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    # res = np.array([])  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    res = np.empty(t.size)  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    for i in range(t.size):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        res[i] = _welsh_old(t1, d1, t2, d2, t[i], dt[i])  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    return res  | 
            
            
                                                                        
                            
            
                                    
            
            
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                @guvectorize([(float64[:], float64[:], float64[:], float64[:], float64[:], float64[:], float64[:])], '(n),(n),(m),(m),(c),(c)->(c)')  | 
            
                            
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                def _kroedel_numba(t1, d1, t2, d2, t, dt, res):  | 
            
                            
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                    """Helper function for kroedel_ab()"""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    d1_mean = np.mean(d1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    d2_mean = np.mean(d2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    d1_std = np.std(d1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    d2_std = np.std(d2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    for k in range(len(t)):  | 
            
                            
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                        N = 0  | 
            
                            
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                        numerator = 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        for i in range(len(t1)):  | 
            
                            
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                            for j in range(len(t2)):   | 
            
                            
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                                if ((t[k] - dt[k] / 2) < (t2[j] - t1[i])) & ((t2[j] - t1[i]) < (t[k] + dt[k] / 2)):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    numerator = numerator + (d1[i]-d1_mean)*(d2[j]-d2_mean)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    N = N + 1  | 
            
                            
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                        res[k] = numerator / N / d1_std / d2_std  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    113
                 | 
                                    
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                def kroedel(t1, d1, t2, d2, t, dt):  | 
            
                            
                    | 
                        
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                     | 
                    
                                                                                                                                                                                                                                                                                                                                                                                                                            
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                     
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                | 
                    114
                 | 
                                    
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                    """Krolik & Edelson (1988) correlation with adaptative binning.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    115
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                    116
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                    This function implements the correlation function proposed by  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    117
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                    Krolik & Edelson (1988), which allows for the computation of  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    118
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                    the correlation for -discrete- signals non-uniformly sampled  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    119
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                    in time.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    120
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                    121
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                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    122
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                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    123
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                    t1 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    124
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                        Times corresponding to the first signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    125
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                    d1 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    126
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                        Values of the first signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    127
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                    t2 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    128
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                        Times corresponding to the second signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    129
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                    d2 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    130
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                        Values of the second signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    131
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                    t  : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    132
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                        Times on which to compute the correlation (binning).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    133
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                    dt : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    134
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                        Size of the bins on which to compute the correlation.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    135
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                    136
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                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    137
                 | 
                                    
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                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    138
                 | 
                                    
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                    res : :class:`~numpy.ndarray` (size `len(t)`)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    139
                 | 
                                    
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                 | 
                        Values of the correlation at the times `t`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    140
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    141
                 | 
                                    
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                    Examples  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    142
                 | 
                                    
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                 | 
                    --------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    143
                 | 
                                    
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                    An example of raw usage would be:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    145
                 | 
                                    
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                    >>> import numpy as np  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
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                 | 
                    >>> from mutis.lib.correlation import kroedel_ab  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
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                 | 
                    >>> t1 = np.linspace(1, 10, 100); s1 = np.sin(t1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
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                    >>> t2 = np.linspace(1, 10, 100); s2 = np.cos(t2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
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                    >>> t = np.linspace(1, 10, 100);  dt = np.full(t.shape, 0.1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
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                 | 
                    >>> kroedel(t1, d1, t2, d2, t, dt)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    152
                 | 
                                    
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                    However, it is recommended to be used as expalined in the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                    standard MUTIS' workflow notebook.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
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                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                    if t.size != dt.size:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                        log.error("Error, t and dt not the same size") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                        return False  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                    if t1.size != d1.size:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                        log.error("Error, t1 and d1 not the same size") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
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                 | 
                        return False  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                    if t2.size != d2.size:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                        log.error("Error, t2 and d2 not the same size") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                        return False  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    165
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                    return _kroedel_numba(t1, d1, t2, d2, t, dt)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
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                | 
                    167
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                @guvectorize([(float64[:], float64[:], float64[:], float64[:], float64[:], float64[:], float64[:])], '(n),(n),(m),(m),(c),(c)->(c)')  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                def _welsh_numba(t1, d1, t2, d2, t, dt, res):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
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                 | 
                    """Helper function for welsh_ab()"""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                    for k in range(len(t)):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
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                 | 
                        N=0  | 
            
                            
                    | 
                        
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                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
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                | 
                    174
                 | 
                                    
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                          | 
            
                            
                    | 
                        
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                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    175
                 | 
                                    
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                 | 
                        d1_M_sum = 0  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    176
                 | 
                                    
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                 | 
                        d1_M_sq_sum = 0  | 
            
                            
                    | 
                        
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                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    177
                 | 
                                    
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                          | 
            
                            
                    | 
                        
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                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    178
                 | 
                                    
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                 | 
                        d2_M_sum = 0  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                        d2_M_sq_sum = 0  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    180
                 | 
                                    
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                 | 
                          | 
            
                            
                    | 
                        
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                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    181
                 | 
                                    
                                                     | 
                
                 | 
                        d1_d2_M_sum = 0  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    182
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    183
                 | 
                                    
                                                     | 
                
                 | 
                        for i in range(len(t1)):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    184
                 | 
                                    
                                                     | 
                
                 | 
                            for j in range(len(t2)):   | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    185
                 | 
                                    
                                                     | 
                
                 | 
                                if ((t[k] - dt[k] / 2) < (t2[j] - t1[i])) & ((t2[j] - t1[i]) < (t[k] + dt[k] / 2)):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    186
                 | 
                                    
                                                     | 
                
                 | 
                                    d1_M_sum = d1_M_sum + d1[i]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    187
                 | 
                                    
                                                     | 
                
                 | 
                                    d2_M_sum = d2_M_sum + d2[j]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    188
                 | 
                                    
                                                     | 
                
                 | 
                                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    189
                 | 
                                    
                                                     | 
                
                 | 
                                    d1_M_sq_sum = d1_M_sq_sum + d1[i]**2  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    190
                 | 
                                    
                                                     | 
                
                 | 
                                    d2_M_sq_sum = d2_M_sq_sum + d2[j]**2  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    191
                 | 
                                    
                                                     | 
                
                 | 
                                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    192
                 | 
                                    
                                                     | 
                
                 | 
                                    d1_d2_M_sum =  d1_d2_M_sum + d1[i]*d2[j]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    193
                 | 
                                    
                                                     | 
                
                 | 
                                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    194
                 | 
                                    
                                                     | 
                
                 | 
                                    N = N + 1  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    195
                 | 
                                    
                                                     | 
                
                 | 
                                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    196
                 | 
                                    
                                                     | 
                
                 | 
                        d1_M_mean = d1_M_sum/N  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    197
                 | 
                                    
                                                     | 
                
                 | 
                        d2_M_mean = d2_M_sum/N  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    198
                 | 
                                    
                                                     | 
                
                 | 
                          | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    199
                 | 
                                    
                                                     | 
                
                 | 
                        d1_M_std = (d1_M_sq_sum / N - d1_M_mean**2)**0.5  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    200
                 | 
                                    
                                                     | 
                
                 | 
                        d2_M_std = (d2_M_sq_sum / N - d2_M_mean**2)**0.5  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    201
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    202
                 | 
                                    
                                                     | 
                
                 | 
                        res[k] = (d1_d2_M_sum/N - d1_M_mean*d2_M_mean) / d1_M_std / d2_M_std  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    203
                 | 
                                    
                                                     | 
                
                 | 
                                     | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    204
                 | 
                                    
                                                     | 
                
                 | 
                def welsh(t1, d1, t2, d2, t, dt):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                                                                                                                                                                            
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    205
                 | 
                                    
                                                     | 
                
                 | 
                    """Welsh (1999) correlation with adaptative binning.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    206
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    207
                 | 
                                    
                                                     | 
                
                 | 
                    This function implements the correlation function proposed  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    208
                 | 
                                    
                                                     | 
                
                 | 
                    by Welsh (1999), which allows for the computation of the correlation  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    209
                 | 
                                    
                                                     | 
                
                 | 
                    for -discrete- signals non-uniformly sampled in time.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    210
                 | 
                                    
                                                     | 
                
                 | 
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                    211
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                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    212
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    213
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                    t1 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    214
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                        Times corresponding to the first signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    215
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                    d1 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    216
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                        Values of the first signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    217
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                    t2 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    218
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                        Times corresponding to the second signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    219
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                    d2 : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    220
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                        Values of the second signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    221
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                    t  : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    222
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                        Times on which to compute the correlation (binning).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    223
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                    dt : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    224
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                        Size of the bins on which to compute the correlation.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    225
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                    226
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                 | 
                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    227
                 | 
                                    
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                 | 
                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    228
                 | 
                                    
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                 | 
                    res : :class:`~numpy.ndarray` (size `len(t)`)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    229
                 | 
                                    
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                        Values of the correlation at the times `t`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    230
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    231
                 | 
                                    
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                 | 
                    Examples  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    232
                 | 
                                    
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                 | 
                    --------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    233
                 | 
                                    
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                 | 
                    An example of raw usage would be:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    234
                 | 
                                    
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    235
                 | 
                                    
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                    >>> import numpy as np  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    236
                 | 
                                    
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                 | 
                    >>> from mutis.lib.correlation import welsh_ab  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    237
                 | 
                                    
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                 | 
                    >>> t1 = np.linspace(1, 10, 100); s1 = np.sin(t1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    238
                 | 
                                    
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                 | 
                    >>> t2 = np.linspace(1, 10, 100); s2 = np.cos(t2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    239
                 | 
                                    
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                 | 
                    >>> t = np.linspace(1, 10, 100);  dt = np.full(t.shape, 0.1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    240
                 | 
                                    
                                                     | 
                
                 | 
                    >>> welsh(t1, d1, t2, d2, t, dt)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    241
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    242
                 | 
                                    
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                    However, it is recommended to be used as expalined in the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    243
                 | 
                                    
                                                     | 
                
                 | 
                    standard MUTIS' workflow notebook.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    244
                 | 
                                    
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                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    245
                 | 
                                    
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                 | 
                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    246
                 | 
                                    
                                                     | 
                
                 | 
                    if t.size != dt.size:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    247
                 | 
                                    
                                                     | 
                
                 | 
                        log.error("Error, t and dt not the same size") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    248
                 | 
                                    
                                                     | 
                
                 | 
                        return False  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    249
                 | 
                                    
                                                     | 
                
                 | 
                    if t1.size != d1.size:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    250
                 | 
                                    
                                                     | 
                
                 | 
                        log.error("Error, t1 and d1 not the same size") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    251
                 | 
                                    
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                 | 
                        return False  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    252
                 | 
                                    
                                                     | 
                
                 | 
                    if t2.size != d2.size:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    253
                 | 
                                    
                                                     | 
                
                 | 
                        log.error("Error, t2 and d2 not the same size") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    254
                 | 
                                    
                                                     | 
                
                 | 
                        return False  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    255
                 | 
                                    
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                 | 
                      | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    256
                 | 
                                    
                                                     | 
                
                 | 
                    return _welsh_numba(t1, d1, t2, d2, t, dt)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    257
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    258
                 | 
                                    
                                                     | 
                
                 | 
                def ndcf(x, y):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    259
                 | 
                                    
                                                     | 
                
                 | 
                    """Computes the normalised correlation of two discrete signals (ignoring times)."""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    260
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    261
                 | 
                                    
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                 | 
                    x = (x - np.mean(x)) / np.std(x) / len(x)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    262
                 | 
                                    
                                                     | 
                
                 | 
                    y = (y - np.mean(y)) / np.std(y)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    263
                 | 
                                    
                                                     | 
                
                 | 
                    return np.correlate(y, x, "full")  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    264
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    265
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    266
                 | 
                                    
                                                     | 
                
                 | 
                def nindcf(t1, s1, t2, s2):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    267
                 | 
                                    
                                                     | 
                
                 | 
                    """Computes the normalised correlation of two discrete signals (interpolating them)."""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    268
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    269
                 | 
                                    
                                                     | 
                
                 | 
                    dt = np.max([(t1.max() - t1.min()) / t1.size, (t2.max() - t2.min()) / t2.size])  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    270
                 | 
                                    
                                                     | 
                
                 | 
                    n1 = np.int(np.ptp(t1) / dt * 10.0)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    271
                 | 
                                    
                                                     | 
                
                 | 
                    n2 = np.int(np.ptp(t1) / dt * 10.0)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    272
                 | 
                                    
                                                     | 
                
                 | 
                    s1i = np.interp(np.linspace(t1.min(), t1.max(), n1), t1, s1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    273
                 | 
                                    
                                                     | 
                
                 | 
                    s2i = np.interp(np.linspace(t2.min(), t2.max(), n2), t2, s2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    274
                 | 
                                    
                                                     | 
                
                 | 
                    return ndcf(s1i, s2i)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    275
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    276
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    277
                 | 
                                    
                                                     | 
                
                 | 
                def gen_times_rawab(t1, t2, dt0=None, ndtmax=1.0, nbinsmin=121, force=None):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    278
                 | 
                                    
                                                     | 
                
                 | 
                    """LEGACY. Returns t, dt for use with adaptative binning methods.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    279
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    280
                 | 
                                    
                                                     | 
                
                 | 
                    Uses a shitty algorithm to find a time binning in which each bin contains  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    281
                 | 
                                    
                                                     | 
                
                 | 
                    a minimum of points (specified by `nbinsmin`, with an starting bin size  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    282
                 | 
                                    
                                                     | 
                
                 | 
                    (`dt0`) and a maximum bin size (`ndtmax*dt0`).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    283
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    284
                 | 
                                    
                                                     | 
                
                 | 
                    The algorithms start at the first time bin, and enlarges the bin size  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    285
                 | 
                                    
                                                     | 
                
                 | 
                    until it has enough points or it reaches the maximum length, then creates  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    286
                 | 
                                    
                                                     | 
                
                 | 
                    another starting at that point.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    287
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    288
                 | 
                                    
                                                     | 
                
                 | 
                    If `force` is True, then it discards the created bins on which there are  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    289
                 | 
                                    
                                                     | 
                
                 | 
                    not enough points.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    290
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    291
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    292
                 | 
                                    
                                                     | 
                
                 | 
                    # Sensible values for these parameters must be found by hand, and depend  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    293
                 | 
                                    
                                                     | 
                
                 | 
                    # on the characteristic of input data.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    294
                 | 
                                    
                                                     | 
                
                 | 
                    #  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    295
                 | 
                                    
                                                     | 
                
                 | 
                    # dt0:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    296
                 | 
                                    
                                                     | 
                
                 | 
                    #     minimum bin size, also used as step in a.b.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    297
                 | 
                                    
                                                     | 
                
                 | 
                    #         default: dt0 = 0.25*(tmax-tmin)/np.sqrt(t1.size*t2.size+1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    298
                 | 
                                    
                                                     | 
                
                 | 
                    #     (more or less a statistically reasonable binning,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    299
                 | 
                                    
                                                     | 
                
                 | 
                    #     to increase precision)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    300
                 | 
                                    
                                                     | 
                
                 | 
                    # ndtmax:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    301
                 | 
                                    
                                                     | 
                
                 | 
                    #     Maximum size of bins (in units of dt0).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    302
                 | 
                                    
                                                     | 
                
                 | 
                    #     default: 1.0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    303
                 | 
                                    
                                                     | 
                
                 | 
                    # nbinsmin:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    304
                 | 
                                    
                                                     | 
                
                 | 
                    #     if the data has a lot of error, higher values are needed  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    305
                 | 
                                    
                                                     | 
                
                 | 
                    #     to soften the correlation beyond spurious variability.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    306
                 | 
                                    
                                                     | 
                
                 | 
                    #         default: 121 (11x11)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    307
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    308
                 | 
                                    
                                                     | 
                
                 | 
                    # tmin = -(np.min([t1.max(),t2.max()]) - np.max([t1.min(),t2.min()]))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    309
                 | 
                                    
                                                     | 
                
                 | 
                    tmax = +(np.max([t1.max(), t2.max()]) - np.min([t1.min(), t2.min()]))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    310
                 | 
                                    
                                                     | 
                
                 | 
                    tmin = -tmax  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    311
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    312
                 | 
                                    
                                                     | 
                
                 | 
                    if dt0 is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    313
                 | 
                                    
                                                     | 
                
                 | 
                        dt0 = 0.25 * (tmax - tmin) / np.sqrt(t1.size * t2.size + 1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    314
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    315
                 | 
                                    
                                                     | 
                
                 | 
                    t = np.array([])  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    316
                 | 
                                    
                                                     | 
                
                 | 
                    dt = np.array([])  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    317
                 | 
                                    
                                                     | 
                
                 | 
                    nb = np.array([])  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    318
                 | 
                                    
                                                     | 
                
                 | 
                    t1m, t2m = np.meshgrid(t1, t2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    319
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    320
                 | 
                                    
                                                     | 
                
                 | 
                    ti = tmin  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    321
                 | 
                                    
                                                     | 
                
                 | 
                    tf = ti + dt0  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    322
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    323
                 | 
                                    
                                                     | 
                
                 | 
                    while tf < tmax:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    324
                 | 
                                    
                                                     | 
                
                 | 
                        tm = (ti + tf) / 2  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    325
                 | 
                                    
                                                     | 
                
                 | 
                        dtm = tf - ti  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    326
                 | 
                                    
                                                     | 
                
                 | 
                        nbins = np.sum((((tm - dtm / 2) < (t2m - t1m)) & ((t2m - t1m) < (tm + dtm / 2))))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    327
                 | 
                                    
                                                     | 
                
                 | 
                        if dtm <= dt0 * ndtmax:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    328
                 | 
                                    
                                                     | 
                
                 | 
                            if nbins >= nbinsmin:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    329
                 | 
                                    
                                                     | 
                
                 | 
                                t = np.append(t, tm)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    330
                 | 
                                    
                                                     | 
                
                 | 
                                dt = np.append(dt, dtm)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    331
                 | 
                                    
                                                     | 
                
                 | 
                                nb = np.append(nb, nbins)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    332
                 | 
                                    
                                                     | 
                
                 | 
                                ti, tf = tf, tf + dt0  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    333
                 | 
                                    
                                                     | 
                
                 | 
                            else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    334
                 | 
                                    
                                                     | 
                
                 | 
                                tf = tf + 0.1 * dt0  # try small increments  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    335
                 | 
                                    
                                                     | 
                
                 | 
                        else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    336
                 | 
                                    
                                                     | 
                
                 | 
                            ti, tf = tf, tf + dt0  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    337
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    338
                 | 
                                    
                                                     | 
                
                 | 
                    # force zero to appear in t ##  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    339
                 | 
                                    
                                                     | 
                
                 | 
                    if force is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    340
                 | 
                                    
                                                     | 
                
                 | 
                        force = [0]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    341
                 | 
                                    
                                                     | 
                
                 | 
                    for tm in force:  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    342
                 | 
                                    
                                                     | 
                
                 | 
                        dtm = dt0 / 2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    343
                 | 
                                    
                                                     | 
                
                 | 
                        nbins = np.sum((((tm - dtm / 2) < (t2m - t1m)) & ((t2m - t1m) < (tm + dtm / 2))))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    344
                 | 
                                    
                                                     | 
                
                 | 
                        while dtm <= dt0 * ndtmax:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    345
                 | 
                                    
                                                     | 
                
                 | 
                            if nbins >= nbinsmin:  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    346
                 | 
                                    
                                                     | 
                
                 | 
                                t = np.append(t, tm)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    347
                 | 
                                    
                                                     | 
                
                 | 
                                dt = np.append(dt, dtm)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    348
                 | 
                                    
                                                     | 
                
                 | 
                                nb = np.append(nb, nbins)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    349
                 | 
                                    
                                                     | 
                
                 | 
                                break  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    350
                 | 
                                    
                                                     | 
                
                 | 
                            else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    351
                 | 
                                    
                                                     | 
                
                 | 
                                dtm = dtm + dt0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    352
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    353
                 | 
                                    
                                                     | 
                
                 | 
                    idx = np.argsort(t)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    354
                 | 
                                    
                                                     | 
                
                 | 
                    t = t[idx]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    355
                 | 
                                    
                                                     | 
                
                 | 
                    dt = dt[idx]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    356
                 | 
                                    
                                                     | 
                
                 | 
                    nb = nb[idx]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    357
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    358
                 | 
                                    
                                                     | 
                
                 | 
                    return t, dt, nb  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    359
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    360
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    361
                 | 
                                    
                                                     | 
                
                 | 
                def gen_times_uniform(t1, t2, dtm=None, tmin=None, tmax=None, nbinsmin=121, n=200):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    362
                 | 
                                    
                                                     | 
                
                 | 
                    """Returns an uniform t, dt time binning for use with adaptative binning methods.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    363
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    364
                 | 
                                    
                                                     | 
                
                 | 
                    The time interval on which the correlation is defined is split in  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    365
                 | 
                                    
                                                     | 
                
                 | 
                    `n` bins. Bins with a number of point less than `nbinsmin` are discarded.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    366
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    367
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    368
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    369
                 | 
                                    
                                                     | 
                
                 | 
                    t1 : :py:class:`np.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    370
                 | 
                                    
                                                     | 
                
                 | 
                        Times of the first signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    371
                 | 
                                    
                                                     | 
                
                 | 
                    t2 : :py:class:`np.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    372
                 | 
                                    
                                                     | 
                
                 | 
                        Times of the second signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    373
                 | 
                                    
                                                     | 
                
                 | 
                    tmin : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    374
                 | 
                                    
                                                     | 
                
                 | 
                        Start of the time intervals (if not specified, start of the interval on which the correlation is define).  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    375
                 | 
                                    
                                                     | 
                
                 | 
                    tmax : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    376
                 | 
                                    
                                                     | 
                
                 | 
                        End of the time intervals (if not specified, end of the interval on which the correlation is define).  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    377
                 | 
                                    
                                                     | 
                
                 | 
                    nbinsmin : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    378
                 | 
                                    
                                                     | 
                
                 | 
                        Minimum of points falling on each bin.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    379
                 | 
                                    
                                                     | 
                
                 | 
                    n : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    380
                 | 
                                    
                                                     | 
                
                 | 
                        Number of bins in which to split (needs not to be the number of bins returned).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    381
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    382
                 | 
                                    
                                                     | 
                
                 | 
                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    383
                 | 
                                    
                                                     | 
                
                 | 
                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    384
                 | 
                                    
                                                     | 
                
                 | 
                    t : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    385
                 | 
                                    
                                                     | 
                
                 | 
                        Time binning on which to compute the correlation.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    386
                 | 
                                    
                                                     | 
                
                 | 
                    dt : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    387
                 | 
                                    
                                                     | 
                
                 | 
                        Size of the bins defined by `t`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    388
                 | 
                                    
                                                     | 
                
                 | 
                    nb : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    389
                 | 
                                    
                                                     | 
                
                 | 
                        Number of points falling on each bin defined by `t` and `dt`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    390
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    391
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    392
                 | 
                                    
                                                     | 
                
                 | 
                    if tmax is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    393
                 | 
                                    
                                                     | 
                
                 | 
                        tmax = +(np.max([t1.max(), t2.max()]) - np.min([t1.min(), t2.min()]))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    394
                 | 
                                    
                                                     | 
                
                 | 
                    if tmin is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    395
                 | 
                                    
                                                     | 
                
                 | 
                        tmin = -tmax  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    396
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    397
                 | 
                                    
                                                     | 
                
                 | 
                    t = np.linspace(tmin, tmax, n)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    398
                 | 
                                    
                                                     | 
                
                 | 
                    if dtm is None:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    399
                 | 
                                    
                                                     | 
                
                 | 
                        dtm = (tmax - tmin) / n  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    400
                 | 
                                    
                                                     | 
                
                 | 
                    dt = np.full(t.shape, dtm)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    401
                 | 
                                    
                                                     | 
                
                 | 
                    nb = np.empty(t.shape)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    402
                 | 
                                    
                                                     | 
                
                 | 
                    t1m, t2m = np.meshgrid(t1, t2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    403
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    404
                 | 
                                    
                                                     | 
                
                 | 
                    for im, tm in enumerate(t):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    405
                 | 
                                    
                                                     | 
                
                 | 
                        nb[im] = np.sum((((tm - dtm / 2) < (t2m - t1m)) & ((t2m - t1m) < (tm + dtm / 2))))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    406
                 | 
                                    
                                                     | 
                
                 | 
                    idx = nb < nbinsmin  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    407
                 | 
                                    
                                                     | 
                
                 | 
                    t = np.delete(t, idx)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    408
                 | 
                                    
                                                     | 
                
                 | 
                    dt = np.delete(dt, idx)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    409
                 | 
                                    
                                                     | 
                
                 | 
                    nb = np.delete(nb, idx)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    410
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    411
                 | 
                                    
                                                     | 
                
                 | 
                    return t, dt, nb  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    412
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    413
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    414
                 | 
                                    
                                                     | 
                
                 | 
                def gen_times_canopy(t1, t2, dtmin=0.01, dtmax=0.5, nbinsmin=500, nf=0.5):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                                                                    
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    415
                 | 
                                    
                                                     | 
                
                 | 
                    """Returns a non-uniform t, dt time binning for use with adaptative binning methods.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    416
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    417
                 | 
                                    
                                                     | 
                
                 | 
                    This cumbersome algorithm does more or less the following:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    418
                 | 
                                    
                                                     | 
                
                 | 
                    1) Divides the time interval on which the correlation is defined in  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    419
                 | 
                                    
                                                     | 
                
                 | 
                    the maximum number of points (minimum bin size defined by `dtmin`).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    420
                 | 
                                    
                                                     | 
                
                 | 
                    2) Checks the number of point falling on each bin.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    421
                 | 
                                    
                                                     | 
                
                 | 
                    3) If there are several consecutive intervals with a number of points  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    422
                 | 
                                    
                                                     | 
                
                 | 
                    over `nbinsmin`, it groups them (reducing the number of points  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    423
                 | 
                                    
                                                     | 
                
                 | 
                    exponentially as defined by `nf`, if the number of intervals in the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    424
                 | 
                                    
                                                     | 
                
                 | 
                    group is high, or one by one if it is low.)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    425
                 | 
                                    
                                                     | 
                
                 | 
                    4) Repeat until APPROXIMATELY we have reached intervals of size `dtmax`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    426
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    427
                 | 
                                    
                                                     | 
                
                 | 
                    How the exact implementation works, I forgot! But the results are more  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    428
                 | 
                                    
                                                     | 
                
                 | 
                    or less nice...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    429
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    430
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    431
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    432
                 | 
                                    
                                                     | 
                
                 | 
                    t1 : :py:class:`np.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    433
                 | 
                                    
                                                     | 
                
                 | 
                        Times of the first signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    434
                 | 
                                    
                                                     | 
                
                 | 
                    t2 : :py:class:`np.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    435
                 | 
                                    
                                                     | 
                
                 | 
                        Times of the second signal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    436
                 | 
                                    
                                                     | 
                
                 | 
                    dtmin : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    437
                 | 
                                    
                                                     | 
                
                 | 
                        Start of the time intervals (if not specified, start of the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    438
                 | 
                                    
                                                     | 
                
                 | 
                        interval on which the correlation is define).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    439
                 | 
                                    
                                                     | 
                
                 | 
                    dtmax : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    440
                 | 
                                    
                                                     | 
                
                 | 
                        End of the time intervals (if not specified, end of the interval  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    441
                 | 
                                    
                                                     | 
                
                 | 
                        on which the correlation is define).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    442
                 | 
                                    
                                                     | 
                
                 | 
                    nbinsmin : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    443
                 | 
                                    
                                                     | 
                
                 | 
                        Minimum of points falling on each bin.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    444
                 | 
                                    
                                                     | 
                
                 | 
                    nf : :py:class:`~float`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    445
                 | 
                                    
                                                     | 
                
                 | 
                        How fast are the intervals divided.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    446
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    447
                 | 
                                    
                                                     | 
                
                 | 
                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    448
                 | 
                                    
                                                     | 
                
                 | 
                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    449
                 | 
                                    
                                                     | 
                
                 | 
                    t : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    450
                 | 
                                    
                                                     | 
                
                 | 
                        Time binning on which to compute the correlation.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    451
                 | 
                                    
                                                     | 
                
                 | 
                    dt : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    452
                 | 
                                    
                                                     | 
                
                 | 
                        Size of the bins defined by `t`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    453
                 | 
                                    
                                                     | 
                
                 | 
                    nb : :class:`~numpy.ndarray`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    454
                 | 
                                    
                                                     | 
                
                 | 
                        Number of points falling on each bin defined by `t` and `dt`.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    455
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    456
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    457
                 | 
                                    
                                                     | 
                
                 | 
                    t1m, t2m = np.meshgrid(t1, t2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    458
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    459
                 | 
                                    
                                                     | 
                
                 | 
                    def _comp_nb(t, dt):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    460
                 | 
                                    
                                                     | 
                
                 | 
                        nb = np.empty(len(t))  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    461
                 | 
                                    
                                                     | 
                
                 | 
                        for i in range(len(t)):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    462
                 | 
                                    
                                                     | 
                
                 | 
                            nb[i] = np.sum(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    463
                 | 
                                    
                                                     | 
                
                 | 
                                (((t[i] - dt[i] / 2) < (t2m - t1m)) & ((t2m - t1m) < (t[i] + dt[i] / 2)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    464
                 | 
                                    
                                                     | 
                
                 | 
                            )  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    465
                 | 
                                    
                                                     | 
                
                 | 
                        return nb  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    466
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    467
                 | 
                                    
                                                     | 
                
                 | 
                    tmax = +(np.max([t1.max(), t2.max()]) - np.min([t1.min(), t2.min()]))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    468
                 | 
                                    
                                                     | 
                
                 | 
                    tmin = -tmax  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    469
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    470
                 | 
                                    
                                                     | 
                
                 | 
                    t = np.linspace(tmin, tmax, int((tmax - tmin) / dtmin))  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    471
                 | 
                                    
                                                     | 
                
                 | 
                    dt = np.full(t.size, np.ptp(t) / t.size)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    472
                 | 
                                    
                                                     | 
                
                 | 
                    nb = _comp_nb(t, dt)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    473
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    474
                 | 
                                    
                                                     | 
                
                 | 
                    k = 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    475
                 | 
                                    
                                                     | 
                
                 | 
                    while k < int(np.log(dtmax / dtmin) / np.log(1 / nf)):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    476
                 | 
                                    
                                                     | 
                
                 | 
                        k = k + 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    477
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    478
                 | 
                                    
                                                     | 
                
                 | 
                        idx = nb < nbinsmin  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    479
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    480
                 | 
                                    
                                                     | 
                
                 | 
                        ts, dts, nbs = t, dt, nb  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    481
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    482
                 | 
                                    
                                                     | 
                
                 | 
                        t, dt = np.copy(ts), np.copy(dts)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    483
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    484
                 | 
                                    
                                                     | 
                
                 | 
                        n_grp = 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    485
                 | 
                                    
                                                     | 
                
                 | 
                        grps = (  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    486
                 | 
                                    
                                                     | 
                
                 | 
                            np.where(np.diff(np.concatenate(([False], idx, [False]), dtype=int)) != 0)[0]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    487
                 | 
                                    
                                                     | 
                
                 | 
                        ).reshape(-1, 2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    488
                 | 
                                    
                                                     | 
                
                 | 
                        for i_grp, grp in enumerate(grps):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    489
                 | 
                                    
                                                     | 
                
                 | 
                            if grp[0] > 0:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    490
                 | 
                                    
                                                     | 
                
                 | 
                                ar = grp[0]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    491
                 | 
                                    
                                                     | 
                
                 | 
                                a = t[grp[0] - 1]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    492
                 | 
                                    
                                                     | 
                
                 | 
                            else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    493
                 | 
                                    
                                                     | 
                
                 | 
                                ar = grp[0]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    494
                 | 
                                    
                                                     | 
                
                 | 
                                a = t[grp[0]]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    495
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    496
                 | 
                                    
                                                     | 
                
                 | 
                            if grp[1] < t.size - 1:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    497
                 | 
                                    
                                                     | 
                
                 | 
                                br = grp[1] - 1  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    498
                 | 
                                    
                                                     | 
                
                 | 
                                b = t[grp[1]]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    499
                 | 
                                    
                                                     | 
                
                 | 
                            else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    500
                 | 
                                    
                                                     | 
                
                 | 
                                br = grp[1] - 1  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    501
                 | 
                                    
                                                     | 
                
                 | 
                                b = t[grp[1] - 1]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    502
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    503
                 | 
                                    
                                                     | 
                
                 | 
                            if (br - ar) < 8:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    504
                 | 
                                    
                                                     | 
                
                 | 
                                if br - ar >= 1:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    505
                 | 
                                    
                                                     | 
                
                 | 
                                    n = br - ar + 1  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    506
                 | 
                                    
                                                     | 
                
                 | 
                                else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    507
                 | 
                                    
                                                     | 
                
                 | 
                                    n = br - ar + 2  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    508
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    509
                 | 
                                    
                                                     | 
                
                 | 
                                tins = np.linspace(a, b, n, endpoint=False)[1:]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    510
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    511
                 | 
                                    
                                                     | 
                
                 | 
                                ts = np.delete(ts, np.arange(ar, br + 1) - n_grp)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    512
                 | 
                                    
                                                     | 
                
                 | 
                                dts = np.delete(dts, np.arange(ar, br + 1) - n_grp)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    513
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    514
                 | 
                                    
                                                     | 
                
                 | 
                                ts = np.insert(ts, grp[0] - n_grp, tins)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    515
                 | 
                                    
                                                     | 
                
                 | 
                                dts = np.insert(dts, grp[0] - n_grp, np.full(n - 1, (b - a) / (n - 1)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    516
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    517
                 | 
                                    
                                                     | 
                
                 | 
                                if br - ar >= 1:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    518
                 | 
                                    
                                                     | 
                
                 | 
                                    n_grp = n_grp + 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    519
                 | 
                                    
                                                     | 
                
                 | 
                                else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    520
                 | 
                                    
                                                     | 
                
                 | 
                                    pass  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    521
                 | 
                                    
                                                     | 
                
                 | 
                            else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    522
                 | 
                                    
                                                     | 
                
                 | 
                                n = int(nf * (br - ar + 1))  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    523
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    524
                 | 
                                    
                                                     | 
                
                 | 
                                tins = np.linspace(a, b, n, endpoint=False)[1:]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    525
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    526
                 | 
                                    
                                                     | 
                
                 | 
                                ts = np.delete(ts, np.arange(ar, br + 1) - n_grp)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    527
                 | 
                                    
                                                     | 
                
                 | 
                                dts = np.delete(dts, np.arange(ar, br + 1) - n_grp)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    528
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    529
                 | 
                                    
                                                     | 
                
                 | 
                                ts = np.insert(ts, grp[0] - n_grp, tins)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    530
                 | 
                                    
                                                     | 
                
                 | 
                                dts = np.insert(dts, grp[0] - n_grp, np.full(n - 1, (b - a) / (n - 1)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    531
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    532
                 | 
                                    
                                                     | 
                
                 | 
                                if br - ar >= 1:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    533
                 | 
                                    
                                                     | 
                
                 | 
                                    n_grp = n_grp + (grp[1] - grp[0] - n) + 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    534
                 | 
                                    
                                                     | 
                
                 | 
                                else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    535
                 | 
                                    
                                                     | 
                
                 | 
                                    pass  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    536
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    537
                 | 
                                    
                                                     | 
                
                 | 
                        t = ts  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    538
                 | 
                                    
                                                     | 
                
                 | 
                        dt = dts  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    539
                 | 
                                    
                                                     | 
                
                 | 
                        nb = _comp_nb(t, dt)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    540
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    541
                 | 
                                    
                                                     | 
                
                 | 
                    idx = nb < nbinsmin  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    542
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    543
                 | 
                                    
                                                     | 
                
                 | 
                    t = np.delete(t, idx)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    544
                 | 
                                    
                                                     | 
                
                 | 
                    dt = np.delete(dt, idx)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    545
                 | 
                                    
                                                     | 
                
                 | 
                    nb = np.delete(nb, idx)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    546
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    547
                 | 
                                    
                                                     | 
                
                 | 
                    return t, dt, nb  | 
            
            
                                                        
            
                                    
            
            
                | 
                    548
                 | 
                                    
                                                     | 
                
                 | 
                 |