| 1 |  |  | # Licensed under a 3-clause BSD style license - see LICENSE | 
            
                                                        
            
                                    
            
            
                | 2 |  |  | """Methods for correlation of light curves.""" | 
            
                                                        
            
                                    
            
            
                | 3 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 4 |  |  | import logging | 
            
                                                        
            
                                    
            
            
                | 5 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 6 |  |  | import numpy as np | 
                            
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                | 7 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 8 |  |  | from mutis.lib.utils import get_grid | 
            
                                                        
            
                                    
            
            
                | 9 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 10 |  |  | __all__ = ["kroedel_ab", "welsh_ab", "nindcf", "gen_times_rawab", "gen_times_uniform", "gen_times_canopy"] | 
                            
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                | 11 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 12 |  |  | log = logging.getLogger(__name__) | 
            
                                                        
            
                                    
            
            
                | 13 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 14 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 15 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 16 |  |  | def kroedel_ab_p(t1, d1, t2, d2, t, dt): | 
                            
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                | 17 |  |  |     """Helper function for kroedel_ab()""" | 
            
                                                        
            
                                    
            
            
                | 18 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 19 |  |  |     t1m, t2m = get_grid(t1, t2) | 
            
                                                        
            
                                    
            
            
                | 20 |  |  |     d1m, d2m = np.meshgrid(d1, d2) | 
            
                                                        
            
                                    
            
            
                | 21 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 22 |  |  |     mask = ((t - dt / 2) < (t2m - t1m)) & ((t2m - t1m) < (t + dt / 2)) | 
            
                                                        
            
                                    
            
            
                | 23 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 24 |  |  |     udcf = (d1m - np.mean(d1)) * (d2m - np.mean(d2)) / np.std(d1) / np.std(d2) | 
            
                                                        
            
                                    
            
            
                | 25 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 26 |  |  |     return np.mean(udcf[mask]) | 
            
                                                        
            
                                    
            
            
                | 27 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 28 |  |  |  | 
            
                                                        
            
                                                                    
                                                                                                        
            
            
                | 29 |  | View Code Duplication | def kroedel_ab(t1, d1, t2, d2, t, dt): | 
                            
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                | 30 |  |  |     """Krolik & Edelson (1988) correlation with adaptative binning. | 
            
                                                        
            
                                    
            
            
                | 31 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 32 |  |  |     This function implements the correlation function proposed by | 
            
                                                        
            
                                    
            
            
                | 33 |  |  |     Krolik & Edelson (1988), which allows for the computation of | 
            
                                                        
            
                                    
            
            
                | 34 |  |  |     the correlation for -discrete- signals non-uniformly sampled | 
            
                                                        
            
                                    
            
            
                | 35 |  |  |     in time. | 
            
                                                        
            
                                    
            
            
                | 36 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 37 |  |  |     Parameters | 
            
                                                        
            
                                    
            
            
                | 38 |  |  |     ---------- | 
            
                                                        
            
                                    
            
            
                | 39 |  |  |     t1 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 40 |  |  |         Times corresponding to the first signal. | 
            
                                                        
            
                                    
            
            
                | 41 |  |  |     d1 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 42 |  |  |         Values of the first signal. | 
            
                                                        
            
                                    
            
            
                | 43 |  |  |     t2 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 44 |  |  |         Times corresponding to the second signal. | 
            
                                                        
            
                                    
            
            
                | 45 |  |  |     d2 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 46 |  |  |         Values of the second signal. | 
            
                                                        
            
                                    
            
            
                | 47 |  |  |     t  : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 48 |  |  |         Times on which to compute the correlation (binning). | 
            
                                                        
            
                                    
            
            
                | 49 |  |  |     dt : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 50 |  |  |         Size of the bins on which to compute the correlation. | 
            
                                                        
            
                                    
            
            
                | 51 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 52 |  |  |     Returns | 
            
                                                        
            
                                    
            
            
                | 53 |  |  |     ------- | 
            
                                                        
            
                                    
            
            
                | 54 |  |  |     res : :class:`~numpy.ndarray` (size `len(t)`) | 
            
                                                        
            
                                    
            
            
                | 55 |  |  |         Values of the correlation at the times `t`. | 
            
                                                        
            
                                    
            
            
                | 56 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 57 |  |  |     Examples | 
            
                                                        
            
                                    
            
            
                | 58 |  |  |     -------- | 
            
                                                        
            
                                    
            
            
                | 59 |  |  |     An example of raw usage would be: | 
            
                                                        
            
                                    
            
            
                | 60 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 61 |  |  |     >>> import numpy as np | 
            
                                                        
            
                                    
            
            
                | 62 |  |  |     >>> from mutis.lib.correlation import kroedel_ab | 
            
                                                        
            
                                    
            
            
                | 63 |  |  |     >>> t1 = np.linspace(1, 10, 100); s1 = np.sin(t1) | 
            
                                                        
            
                                    
            
            
                | 64 |  |  |     >>> t2 = np.linspace(1, 10, 100); s2 = np.cos(t2) | 
            
                                                        
            
                                    
            
            
                | 65 |  |  |     >>> t = np.linspace(1, 10, 100);  dt = np.full(t.shape, 0.1) | 
            
                                                        
            
                                    
            
            
                | 66 |  |  |     >>> kroedel_ab_p(t1, d1, t2, d2, t, dt) | 
            
                                                        
            
                                    
            
            
                | 67 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 68 |  |  |     However, it is recommended to be used as expalined in the | 
            
                                                        
            
                                    
            
            
                | 69 |  |  |     standard MUTIS' workflow notebook. | 
            
                                                        
            
                                    
            
            
                | 70 |  |  |     """ | 
            
                                                        
            
                                    
            
            
                | 71 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 72 |  |  |     if t.size != dt.size: | 
            
                                                        
            
                                    
            
            
                | 73 |  |  |         log.error("Error, t and dt not the same size") | 
            
                                                        
            
                                    
            
            
                | 74 |  |  |         return False | 
            
                                                        
            
                                    
            
            
                | 75 |  |  |     if t1.size != d1.size: | 
            
                                                        
            
                                    
            
            
                | 76 |  |  |         log.error("Error, t1 and d1 not the same size") | 
            
                                                        
            
                                    
            
            
                | 77 |  |  |         return False | 
            
                                                        
            
                                    
            
            
                | 78 |  |  |     if t2.size != d2.size: | 
            
                                                        
            
                                    
            
            
                | 79 |  |  |         log.error("Error, t2 and d2 not the same size") | 
            
                                                        
            
                                    
            
            
                | 80 |  |  |         return False | 
            
                                                        
            
                                    
            
            
                | 81 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 82 |  |  |     res = np.empty(t.size) | 
            
                                                        
            
                                    
            
            
                | 83 |  |  |     for i in range(t.size): | 
            
                                                        
            
                                    
            
            
                | 84 |  |  |         res[i] = kroedel_ab_p(t1, d1, t2, d2, t[i], dt[i]) | 
            
                                                        
            
                                    
            
            
                | 85 |  |  |     return res | 
            
                                                        
            
                                    
            
            
                | 86 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 87 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 88 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 89 |  |  | def welsh_ab_p(t1, d1, t2, d2, t, dt): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
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                | 90 |  |  |     """Helper function for welsh_ab()""" | 
            
                                                        
            
                                    
            
            
                | 91 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 92 |  |  |     t1m, t2m = get_grid(t1, t2) | 
            
                                                        
            
                                    
            
            
                | 93 |  |  |     d1m, d2m = np.meshgrid(d1, d2) | 
            
                                                        
            
                                    
            
            
                | 94 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 95 |  |  |     msk = ((t - dt / 2) < (t2m - t1m)) & ((t2m - t1m) < (t + dt / 2)) | 
            
                                                        
            
                                    
            
            
                | 96 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 97 |  |  |     udcf = (d1m - np.mean(d1m[msk])) * (d2m - np.mean(d2m[msk])) / np.std(d1m[msk]) / np.std(d2m[msk]) | 
                            
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                | 98 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 99 |  |  |     return np.mean(udcf[msk]) | 
            
                                                        
            
                                    
            
            
                | 100 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 101 |  |  |  | 
            
                                                        
            
                                                                    
                                                                                                        
            
            
                | 102 |  | View Code Duplication | def welsh_ab(t1, d1, t2, d2, t, dt): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                            
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                | 103 |  |  |     """Welsh (1999) correlation with adaptative binning. | 
            
                                                        
            
                                    
            
            
                | 104 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 105 |  |  |     This function implements the correlation function proposed | 
            
                                                        
            
                                    
            
            
                | 106 |  |  |     by Welsh (1999), which allows for the computation of the correlation | 
            
                                                        
            
                                    
            
            
                | 107 |  |  |     for -discrete- signals non-uniformly sampled in time. | 
            
                                                        
            
                                    
            
            
                | 108 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 109 |  |  |     Parameters | 
            
                                                        
            
                                    
            
            
                | 110 |  |  |     ---------- | 
            
                                                        
            
                                    
            
            
                | 111 |  |  |     t1 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 112 |  |  |         Times corresponding to the first signal. | 
            
                                                        
            
                                    
            
            
                | 113 |  |  |     d1 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 114 |  |  |         Values of the first signal. | 
            
                                                        
            
                                    
            
            
                | 115 |  |  |     t2 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 116 |  |  |         Times corresponding to the second signal. | 
            
                                                        
            
                                    
            
            
                | 117 |  |  |     d2 : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 118 |  |  |         Values of the second signal. | 
            
                                                        
            
                                    
            
            
                | 119 |  |  |     t  : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 120 |  |  |         Times on which to compute the correlation (binning). | 
            
                                                        
            
                                    
            
            
                | 121 |  |  |     dt : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 122 |  |  |         Size of the bins on which to compute the correlation. | 
            
                                                        
            
                                    
            
            
                | 123 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 124 |  |  |     Returns | 
            
                                                        
            
                                    
            
            
                | 125 |  |  |     ------- | 
            
                                                        
            
                                    
            
            
                | 126 |  |  |     res : :class:`~numpy.ndarray` (size `len(t)`) | 
            
                                                        
            
                                    
            
            
                | 127 |  |  |         Values of the correlation at the times `t`. | 
            
                                                        
            
                                    
            
            
                | 128 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 129 |  |  |     Examples | 
            
                                                        
            
                                    
            
            
                | 130 |  |  |     -------- | 
            
                                                        
            
                                    
            
            
                | 131 |  |  |     An example of raw usage would be: | 
            
                                                        
            
                                    
            
            
                | 132 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 133 |  |  |     >>> import numpy as np | 
            
                                                        
            
                                    
            
            
                | 134 |  |  |     >>> from mutis.lib.correlation import welsh_ab | 
            
                                                        
            
                                    
            
            
                | 135 |  |  |     >>> t1 = np.linspace(1, 10, 100); s1 = np.sin(t1) | 
            
                                                        
            
                                    
            
            
                | 136 |  |  |     >>> t2 = np.linspace(1, 10, 100); s2 = np.cos(t2) | 
            
                                                        
            
                                    
            
            
                | 137 |  |  |     >>> t = np.linspace(1, 10, 100);  dt = np.full(t.shape, 0.1) | 
            
                                                        
            
                                    
            
            
                | 138 |  |  |     >>> welsh_ab_p(t1, d1, t2, d2, t, dt) | 
            
                                                        
            
                                    
            
            
                | 139 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 140 |  |  |     However, it is recommended to be used as expalined in the | 
            
                                                        
            
                                    
            
            
                | 141 |  |  |     standard MUTIS' workflow notebook. | 
            
                                                        
            
                                    
            
            
                | 142 |  |  |     """ | 
            
                                                        
            
                                    
            
            
                | 143 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 144 |  |  |     if t.size != dt.size: | 
            
                                                        
            
                                    
            
            
                | 145 |  |  |         log.error("Error, t and dt not the same size") | 
            
                                                        
            
                                    
            
            
                | 146 |  |  |         return False | 
            
                                                        
            
                                    
            
            
                | 147 |  |  |     if t1.size != d1.size: | 
            
                                                        
            
                                    
            
            
                | 148 |  |  |         log.error("Error, t1 and d1 not the same size") | 
            
                                                        
            
                                    
            
            
                | 149 |  |  |         return False | 
            
                                                        
            
                                    
            
            
                | 150 |  |  |     if t2.size != d2.size: | 
            
                                                        
            
                                    
            
            
                | 151 |  |  |         log.error("Error, t2 and d2 not the same size") | 
            
                                                        
            
                                    
            
            
                | 152 |  |  |         return False | 
            
                                                        
            
                                    
            
            
                | 153 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 154 |  |  |     # res = np.array([]) | 
            
                                                        
            
                                    
            
            
                | 155 |  |  |     res = np.empty(t.size) | 
            
                                                        
            
                                    
            
            
                | 156 |  |  |     for i in range(t.size): | 
            
                                                        
            
                                    
            
            
                | 157 |  |  |         res[i] = welsh_ab_p(t1, d1, t2, d2, t[i], dt[i]) | 
            
                                                        
            
                                    
            
            
                | 158 |  |  |     return res | 
            
                                                        
            
                                    
            
            
                | 159 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 160 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 161 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 162 |  |  | def ndcf(x, y): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
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                | 163 |  |  |     """Computes the normalised correlation of two discrete signals (ignoring times).""" | 
            
                                                        
            
                                    
            
            
                | 164 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 165 |  |  |     x = (x - np.mean(x)) / np.std(x) / len(x) | 
            
                                                        
            
                                    
            
            
                | 166 |  |  |     y = (y - np.mean(y)) / np.std(y) | 
            
                                                        
            
                                    
            
            
                | 167 |  |  |     return np.correlate(y, x, "full") | 
            
                                                        
            
                                    
            
            
                | 168 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 169 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 170 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 171 |  |  | def nindcf(t1, s1, t2, s2): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                            
                                                                                            
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                | 172 |  |  |     """Computes the normalised correlation of two discrete signals (interpolating them).""" | 
            
                                                        
            
                                    
            
            
                | 173 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 174 |  |  |     dt = np.max([(t1.max() - t1.min()) / t1.size, (t2.max() - t2.min()) / t2.size]) | 
                            
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                | 175 |  |  |     n1 = np.int(np.ptp(t1) / dt * 10.0) | 
                            
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                | 176 |  |  |     n2 = np.int(np.ptp(t1) / dt * 10.0) | 
                            
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                | 177 |  |  |     s1i = np.interp(np.linspace(t1.min(), t1.max(), n1), t1, s1) | 
            
                                                        
            
                                    
            
            
                | 178 |  |  |     s2i = np.interp(np.linspace(t2.min(), t2.max(), n2), t2, s2) | 
            
                                                        
            
                                    
            
            
                | 179 |  |  |     return ndcf(s1i, s2i) | 
            
                                                        
            
                                    
            
            
                | 180 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 181 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 182 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 183 |  |  | def gen_times_rawab(t1, t2, dt0=None, ndtmax=1.0, nbinsmin=121, force=None): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                            
                                                                                            
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                | 184 |  |  |     """LEGACY. Returns t, dt for use with adaptative binning methods. | 
            
                                                        
            
                                    
            
            
                | 185 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 186 |  |  |     Uses a shitty algorithm to find a time binning in which each bin contains | 
            
                                                        
            
                                    
            
            
                | 187 |  |  |     a minimum of points (specified by `nbinsmin`, with an starting bin size | 
            
                                                        
            
                                    
            
            
                | 188 |  |  |     (`dt0`) and a maximum bin size (`ndtmax*dt0`). | 
            
                                                        
            
                                    
            
            
                | 189 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 190 |  |  |     The algorithms start at the first time bin, and enlarges the bin size | 
            
                                                        
            
                                    
            
            
                | 191 |  |  |     until it has enough points or it reaches the maximum length, then creates | 
            
                                                        
            
                                    
            
            
                | 192 |  |  |     another starting at that point. | 
            
                                                        
            
                                    
            
            
                | 193 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 194 |  |  |     If `force` is True, then it discards the created bins on which there are | 
            
                                                        
            
                                    
            
            
                | 195 |  |  |     not enough points. | 
            
                                                        
            
                                    
            
            
                | 196 |  |  |     """ | 
            
                                                        
            
                                    
            
            
                | 197 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 198 |  |  |     # Sensible values for these parameters must be found by hand, and depend | 
            
                                                        
            
                                    
            
            
                | 199 |  |  |     # on the characteristic of input data. | 
            
                                                        
            
                                    
            
            
                | 200 |  |  |     # | 
            
                                                        
            
                                    
            
            
                | 201 |  |  |     # dt0: | 
            
                                                        
            
                                    
            
            
                | 202 |  |  |     #     minimum bin size, also used as step in a.b. | 
            
                                                        
            
                                    
            
            
                | 203 |  |  |     #         default: dt0 = 0.25*(tmax-tmin)/np.sqrt(t1.size*t2.size+1) | 
            
                                                        
            
                                    
            
            
                | 204 |  |  |     #     (more or less a statistically reasonable binning, | 
            
                                                        
            
                                    
            
            
                | 205 |  |  |     #     to increase precision) | 
            
                                                        
            
                                    
            
            
                | 206 |  |  |     # ndtmax: | 
            
                                                        
            
                                    
            
            
                | 207 |  |  |     #     Maximum size of bins (in units of dt0). | 
            
                                                        
            
                                    
            
            
                | 208 |  |  |     #     default: 1.0 | 
            
                                                        
            
                                    
            
            
                | 209 |  |  |     # nbinsmin: | 
            
                                                        
            
                                    
            
            
                | 210 |  |  |     #     if the data has a lot of error, higher values are needed | 
            
                                                        
            
                                    
            
            
                | 211 |  |  |     #     to soften the correlation beyond spurious variability. | 
            
                                                        
            
                                    
            
            
                | 212 |  |  |     #         default: 121 (11x11) | 
            
                                                        
            
                                    
            
            
                | 213 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 214 |  |  |     # tmin = -(np.min([t1.max(),t2.max()]) - np.max([t1.min(),t2.min()])) | 
            
                                                        
            
                                    
            
            
                | 215 |  |  |     tmax = +(np.max([t1.max(), t2.max()]) - np.min([t1.min(), t2.min()])) | 
            
                                                        
            
                                    
            
            
                | 216 |  |  |     tmin = -tmax | 
            
                                                        
            
                                    
            
            
                | 217 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 218 |  |  |     if dt0 is None: | 
            
                                                        
            
                                    
            
            
                | 219 |  |  |         dt0 = 0.25 * (tmax - tmin) / np.sqrt(t1.size * t2.size + 1) | 
            
                                                        
            
                                    
            
            
                | 220 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 221 |  |  |     t = np.array([]) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 222 |  |  |     dt = np.array([]) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 223 |  |  |     nb = np.array([]) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 224 |  |  |     t1m, t2m = np.meshgrid(t1, t2) | 
            
                                                        
            
                                    
            
            
                | 225 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 226 |  |  |     ti = tmin | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 227 |  |  |     tf = ti + dt0 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 228 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 229 |  |  |     while tf < tmax: | 
            
                                                        
            
                                    
            
            
                | 230 |  |  |         tm = (ti + tf) / 2 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 231 |  |  |         dtm = tf - ti | 
            
                                                        
            
                                    
            
            
                | 232 |  |  |         nbins = np.sum((((tm - dtm / 2) < (t2m - t1m)) & ((t2m - t1m) < (tm + dtm / 2)))) | 
            
                                                        
            
                                    
            
            
                | 233 |  |  |         if dtm <= dt0 * ndtmax: | 
            
                                                        
            
                                    
            
            
                | 234 |  |  |             if nbins >= nbinsmin: | 
            
                                                        
            
                                    
            
            
                | 235 |  |  |                 t = np.append(t, tm) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 236 |  |  |                 dt = np.append(dt, dtm) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 237 |  |  |                 nb = np.append(nb, nbins) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 238 |  |  |                 ti, tf = tf, tf + dt0 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 239 |  |  |             else: | 
            
                                                        
            
                                    
            
            
                | 240 |  |  |                 tf = tf + 0.1 * dt0  # try small increments | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 241 |  |  |         else: | 
            
                                                        
            
                                    
            
            
                | 242 |  |  |             ti, tf = tf, tf + dt0 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 243 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 244 |  |  |     # force zero to appear in t ## | 
            
                                                        
            
                                    
            
            
                | 245 |  |  |     if force is None: | 
            
                                                        
            
                                    
            
            
                | 246 |  |  |         force = [0] | 
            
                                                        
            
                                    
            
            
                | 247 |  |  |     for tm in force: | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 248 |  |  |         dtm = dt0 / 2 | 
            
                                                        
            
                                    
            
            
                | 249 |  |  |         nbins = np.sum((((tm - dtm / 2) < (t2m - t1m)) & ((t2m - t1m) < (tm + dtm / 2)))) | 
            
                                                        
            
                                    
            
            
                | 250 |  |  |         while dtm <= dt0 * ndtmax: | 
            
                                                        
            
                                    
            
            
                | 251 |  |  |             if nbins >= nbinsmin: | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 252 |  |  |                 t = np.append(t, tm) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 253 |  |  |                 dt = np.append(dt, dtm) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 254 |  |  |                 nb = np.append(nb, nbins) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 255 |  |  |                 break | 
            
                                                        
            
                                    
            
            
                | 256 |  |  |             else: | 
            
                                                        
            
                                    
            
            
                | 257 |  |  |                 dtm = dtm + dt0 | 
            
                                                        
            
                                    
            
            
                | 258 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 259 |  |  |     idx = np.argsort(t) | 
            
                                                        
            
                                    
            
            
                | 260 |  |  |     t = t[idx] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 261 |  |  |     dt = dt[idx] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 262 |  |  |     nb = nb[idx] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 263 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 264 |  |  |     return t, dt, nb | 
            
                                                        
            
                                    
            
            
                | 265 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 266 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 267 |  |  | def gen_times_uniform(t1, t2, tmin=None, tmax=None, nbinsmin=121, n=200): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 268 |  |  |     """Returns an uniform t, dt time binning for use with adaptative binning methods. | 
            
                                                        
            
                                    
            
            
                | 269 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 270 |  |  |     The time interval on which the correlation is defined is split in | 
            
                                                        
            
                                    
            
            
                | 271 |  |  |     `n` bins. Bins with a number of point less than `nbinsmin` are discarded. | 
            
                                                        
            
                                    
            
            
                | 272 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 273 |  |  |     Parameters | 
            
                                                        
            
                                    
            
            
                | 274 |  |  |     ---------- | 
            
                                                        
            
                                    
            
            
                | 275 |  |  |     t1 : :py:class:`np.ndarray` | 
            
                                                        
            
                                    
            
            
                | 276 |  |  |         Times of the first signal. | 
            
                                                        
            
                                    
            
            
                | 277 |  |  |     t2 : :py:class:`np.ndarray` | 
            
                                                        
            
                                    
            
            
                | 278 |  |  |         Times of the second signal. | 
            
                                                        
            
                                    
            
            
                | 279 |  |  |     tmin : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 280 |  |  |         Start of the time intervals (if not specified, start of the interval on which the correlation is define). | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 281 |  |  |     tmax : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 282 |  |  |         End of the time intervals (if not specified, end of the interval on which the correlation is define). | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 283 |  |  |     nbinsmin : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 284 |  |  |         Minimum of points falling on each bin. | 
            
                                                        
            
                                    
            
            
                | 285 |  |  |     n : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 286 |  |  |         Number of bins in which to split (needs not to be the number of bins returned). | 
            
                                                        
            
                                    
            
            
                | 287 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 288 |  |  |     Returns | 
            
                                                        
            
                                    
            
            
                | 289 |  |  |     ------- | 
            
                                                        
            
                                    
            
            
                | 290 |  |  |     t : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 291 |  |  |         Time binning on which to compute the correlation. | 
            
                                                        
            
                                    
            
            
                | 292 |  |  |     dt : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 293 |  |  |         Size of the bins defined by `t` | 
            
                                                        
            
                                    
            
            
                | 294 |  |  |     nb : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 295 |  |  |         Number of points falling on each bin defined by `t` and `dt`. | 
            
                                                        
            
                                    
            
            
                | 296 |  |  |     """ | 
            
                                                        
            
                                    
            
            
                | 297 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 298 |  |  |     if tmax is None: | 
            
                                                        
            
                                    
            
            
                | 299 |  |  |         tmax = +(np.max([t1.max(), t2.max()]) - np.min([t1.min(), t2.min()])) | 
            
                                                        
            
                                    
            
            
                | 300 |  |  |     if tmin is None: | 
            
                                                        
            
                                    
            
            
                | 301 |  |  |         tmin = -tmax | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 302 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 303 |  |  |     t = np.linspace(tmin, tmax, n) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 304 |  |  |     dtm = (tmax - tmin) / n | 
            
                                                        
            
                                    
            
            
                | 305 |  |  |     dt = np.full(t.shape, dtm) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 306 |  |  |     nb = np.empty(t.shape) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 307 |  |  |     t1m, t2m = np.meshgrid(t1, t2) | 
            
                                                        
            
                                    
            
            
                | 308 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 309 |  |  |     for im, tm in enumerate(t): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 310 |  |  |         nb[im] = np.sum((((tm - dtm / 2) < (t2m - t1m)) & ((t2m - t1m) < (tm + dtm / 2)))) | 
            
                                                        
            
                                    
            
            
                | 311 |  |  |     idx = nb < nbinsmin | 
            
                                                        
            
                                    
            
            
                | 312 |  |  |     t = np.delete(t, idx) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 313 |  |  |     dt = np.delete(dt, idx) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 314 |  |  |     nb = np.delete(nb, idx) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 315 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 316 |  |  |     return t, dt, nb | 
            
                                                        
            
                                    
            
            
                | 317 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 318 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 319 |  |  | def gen_times_canopy(t1, t2, dtmin=0.01, dtmax=0.5, nbinsmin=500, nf=0.5): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 320 |  |  |     """Returns a non-uniform t, dt time binning for use with adaptative binning methods. | 
            
                                                        
            
                                    
            
            
                | 321 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 322 |  |  |     This cumbersome algorithm does more or less the following: | 
            
                                                        
            
                                    
            
            
                | 323 |  |  |     1) Divides the time interval on which the correlation is defined in | 
            
                                                        
            
                                    
            
            
                | 324 |  |  |     the maximum number of points (minimum bin size defined by `dtmin`). | 
            
                                                        
            
                                    
            
            
                | 325 |  |  |     2) Checks the number of point falling on each bin. | 
            
                                                        
            
                                    
            
            
                | 326 |  |  |     3) If there are several consecutive intervals with a number of points | 
            
                                                        
            
                                    
            
            
                | 327 |  |  |     over `nbinsmin`, it groups them (reducing the number of points | 
            
                                                        
            
                                    
            
            
                | 328 |  |  |     exponentially as defined by `nf`, if the number of intervals in the | 
            
                                                        
            
                                    
            
            
                | 329 |  |  |     group is high, or one by one if it is low.) | 
            
                                                        
            
                                    
            
            
                | 330 |  |  |     4) Repeat until APPROXIMATELY we have reached intervals of size `dtmax`. | 
            
                                                        
            
                                    
            
            
                | 331 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 332 |  |  |     How the exact implementation works, I forgot! But the results are more | 
            
                                                        
            
                                    
            
            
                | 333 |  |  |     or less nice... | 
            
                                                        
            
                                    
            
            
                | 334 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 335 |  |  |     Parameters | 
            
                                                        
            
                                    
            
            
                | 336 |  |  |     ---------- | 
            
                                                        
            
                                    
            
            
                | 337 |  |  |     t1 : :py:class:`np.ndarray` | 
            
                                                        
            
                                    
            
            
                | 338 |  |  |         Times of the first signal. | 
            
                                                        
            
                                    
            
            
                | 339 |  |  |     t2 : :py:class:`np.ndarray` | 
            
                                                        
            
                                    
            
            
                | 340 |  |  |         Times of the second signal. | 
            
                                                        
            
                                    
            
            
                | 341 |  |  |     dtmin : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 342 |  |  |         Start of the time intervals (if not specified, start of the | 
            
                                                        
            
                                    
            
            
                | 343 |  |  |         interval on which the correlation is define). | 
            
                                                        
            
                                    
            
            
                | 344 |  |  |     dtmax : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 345 |  |  |         End of the time intervals (if not specified, end of the interval | 
            
                                                        
            
                                    
            
            
                | 346 |  |  |         on which the correlation is define). | 
            
                                                        
            
                                    
            
            
                | 347 |  |  |     nbinsmin : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 348 |  |  |         Minimum of points falling on each bin. | 
            
                                                        
            
                                    
            
            
                | 349 |  |  |     nf : :py:class:`~float` | 
            
                                                        
            
                                    
            
            
                | 350 |  |  |         How fast are the intervals divided. | 
            
                                                        
            
                                    
            
            
                | 351 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 352 |  |  |     Returns | 
            
                                                        
            
                                    
            
            
                | 353 |  |  |     ------- | 
            
                                                        
            
                                    
            
            
                | 354 |  |  |     t : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 355 |  |  |         Time binning on which to compute the correlation. | 
            
                                                        
            
                                    
            
            
                | 356 |  |  |     dt : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 357 |  |  |         Size of the bins defined by `t` | 
            
                                                        
            
                                    
            
            
                | 358 |  |  |     nb : :class:`~numpy.ndarray` | 
            
                                                        
            
                                    
            
            
                | 359 |  |  |         Number of points falling on each bin defined by `t` and `dt`. | 
            
                                                        
            
                                    
            
            
                | 360 |  |  |     """ | 
            
                                                        
            
                                    
            
            
                | 361 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 362 |  |  |     t1m, t2m = np.meshgrid(t1, t2) | 
            
                                                        
            
                                    
            
            
                | 363 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 364 |  |  |     def _comp_nb(t, dt): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 365 |  |  |         nb = np.empty(len(t)) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 366 |  |  |         for i in range(len(t)): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 367 |  |  |             nb[i] = np.sum((((t[i] - dt[i] / 2) < (t2m - t1m)) & ((t2m - t1m) < (t[i] + dt[i] / 2)))) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 368 |  |  |         return nb | 
            
                                                        
            
                                    
            
            
                | 369 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 370 |  |  |     tmax = +(np.max([t1.max(), t2.max()]) - np.min([t1.min(), t2.min()])) | 
            
                                                        
            
                                    
            
            
                | 371 |  |  |     tmin = -tmax | 
            
                                                        
            
                                    
            
            
                | 372 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 373 |  |  |     t = np.linspace(tmin, tmax, int((tmax - tmin) / dtmin)) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 374 |  |  |     dt = np.full(t.size, np.ptp(t) / t.size) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 375 |  |  |     nb = _comp_nb(t, dt) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 376 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 377 |  |  |     k = 0 | 
            
                                                        
            
                                    
            
            
                | 378 |  |  |     while k < int(np.log(dtmax / dtmin) / np.log(1 / nf)): | 
            
                                                        
            
                                    
            
            
                | 379 |  |  |         k = k + 1 | 
            
                                                        
            
                                    
            
            
                | 380 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 381 |  |  |         idx = nb < nbinsmin | 
            
                                                        
            
                                    
            
            
                | 382 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 383 |  |  |         ts, dts, nbs = t, dt, nb | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 384 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 385 |  |  |         t, dt = np.copy(ts), np.copy(dts) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 386 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 387 |  |  |         n_grp = 0 | 
            
                                                        
            
                                    
            
            
                | 388 |  |  |         grps = (np.where(np.diff(np.concatenate(([False], idx, [False]), dtype=int)) != 0)[0]).reshape(-1, 2) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                            
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 389 |  |  |         for i_grp, grp in enumerate(grps): | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 390 |  |  |             if grp[0] > 0: | 
            
                                                        
            
                                    
            
            
                | 391 |  |  |                 ar = grp[0] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 392 |  |  |                 a = t[grp[0] - 1] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 393 |  |  |             else: | 
            
                                                        
            
                                    
            
            
                | 394 |  |  |                 ar = grp[0] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 395 |  |  |                 a = t[grp[0]] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 396 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 397 |  |  |             if grp[1] < t.size - 1: | 
            
                                                        
            
                                    
            
            
                | 398 |  |  |                 br = grp[1] - 1 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 399 |  |  |                 b = t[grp[1]] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 400 |  |  |             else: | 
            
                                                        
            
                                    
            
            
                | 401 |  |  |                 br = grp[1] - 1 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 402 |  |  |                 b = t[grp[1] - 1] | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 403 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 404 |  |  |             if (br - ar) < 8: | 
            
                                                        
            
                                    
            
            
                | 405 |  |  |                 if br - ar >= 1: | 
            
                                                        
            
                                    
            
            
                | 406 |  |  |                     n = br - ar + 1 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 407 |  |  |                 else: | 
            
                                                        
            
                                    
            
            
                | 408 |  |  |                     n = br - ar + 2 | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 409 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 410 |  |  |                 tins = np.linspace(a, b, n, endpoint=False)[1:] | 
            
                                                        
            
                                    
            
            
                | 411 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 412 |  |  |                 ts = np.delete(ts, np.arange(ar, br + 1) - n_grp) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 413 |  |  |                 dts = np.delete(dts, np.arange(ar, br + 1) - n_grp) | 
            
                                                        
            
                                    
            
            
                | 414 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 415 |  |  |                 ts = np.insert(ts, grp[0] - n_grp, tins) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 416 |  |  |                 dts = np.insert(dts, grp[0] - n_grp, np.full(n - 1, (b - a) / (n - 1))) | 
            
                                                        
            
                                    
            
            
                | 417 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 418 |  |  |                 if br - ar >= 1: | 
            
                                                        
            
                                    
            
            
                | 419 |  |  |                     n_grp = n_grp + 1 | 
            
                                                        
            
                                    
            
            
                | 420 |  |  |                 else: | 
            
                                                        
            
                                    
            
            
                | 421 |  |  |                     pass | 
            
                                                        
            
                                    
            
            
                | 422 |  |  |             else: | 
            
                                                        
            
                                    
            
            
                | 423 |  |  |                 n = int(nf * (br - ar + 1)) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 424 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 425 |  |  |                 tins = np.linspace(a, b, n, endpoint=False)[1:] | 
            
                                                        
            
                                    
            
            
                | 426 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 427 |  |  |                 ts = np.delete(ts, np.arange(ar, br + 1) - n_grp) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 428 |  |  |                 dts = np.delete(dts, np.arange(ar, br + 1) - n_grp) | 
            
                                                        
            
                                    
            
            
                | 429 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 430 |  |  |                 ts = np.insert(ts, grp[0] - n_grp, tins) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 431 |  |  |                 dts = np.insert(dts, grp[0] - n_grp, np.full(n - 1, (b - a) / (n - 1))) | 
            
                                                        
            
                                    
            
            
                | 432 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 433 |  |  |                 if br - ar >= 1: | 
            
                                                        
            
                                    
            
            
                | 434 |  |  |                     n_grp = n_grp + (grp[1] - grp[0] - n) + 1 | 
            
                                                        
            
                                    
            
            
                | 435 |  |  |                 else: | 
            
                                                        
            
                                    
            
            
                | 436 |  |  |                     pass | 
            
                                                        
            
                                    
            
            
                | 437 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 438 |  |  |         t = ts | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 439 |  |  |         dt = dts | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 440 |  |  |         nb = _comp_nb(t, dt) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 441 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 442 |  |  |     idx = nb < nbinsmin | 
            
                                                        
            
                                    
            
            
                | 443 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 444 |  |  |     t = np.delete(t, idx) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 445 |  |  |     dt = np.delete(dt, idx) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 446 |  |  |     nb = np.delete(nb, idx) | 
                            
                    |  |  |  | 
                                                                                        
                                                                                     | 
            
                                                        
            
                                    
            
            
                | 447 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 448 |  |  |     return t, dt, nb | 
            
                                                        
            
                                    
            
            
                | 449 |  |  |  |