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# Licensed under a 3-clause BSD style license - see LICENSE |
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"""Analysis of correlation of light curves.""" |
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import logging |
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import matplotlib.pyplot as plt |
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import numpy as np |
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import scipy as sp |
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from mutis.lib.correlation import * |
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from mutis.lib.utils import interp_smooth_curve |
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__all__ = ["Correlation"] |
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log = logging.getLogger(__name__) |
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class Correlation: |
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"""Analysis of the correlation of two signals. |
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Parameters |
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---------- |
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signal1 : :class:`~mutis.signal.Signal` |
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Values of the time axis. |
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signal2 : :class:`~mutis.signal.Signal` |
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Values of the signal axis. |
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fcorr : :py:class:`~str` |
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Method used to correlate the signals. |
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""" |
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def __init__(self, signal1, signal2, fcorr): |
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self.signal1 = signal1 |
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self.signal2 = signal2 |
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self.fcorr = fcorr |
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self.times = np.array([]) |
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self.dts = np.array([]) |
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self.nb = np.array([]) |
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self.values = None |
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# TODO: have a much smaller set of attributes |
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self.samples = None |
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# storage of the significance limits of the correlation |
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self.l1s = None |
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self.l2s = None |
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self.l3s = None |
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# storage of the uncertainties of the correlation |
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self.s1s = None |
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self.s2s = None |
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self.s3s = None |
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# attributes indicating the ranges where the correlations are defined |
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t1, t2 = self.signal1.times, self.signal2.times |
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self.tmin_full = t2.min() - t1.max() |
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self.tmax_full = t2.max() - t1.min() |
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self.t0_full = (self.tmax_full + self.tmin_full) / 2 |
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self.tmin_same = -(np.max([t1.max() - t1.min(), t2.max() - t2.min()])) / 2 + self.t0_full |
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self.tmax_same = (np.max([t1.max() - t1.min(), t2.max() - t2.min()])) / 2 + self.t0_full |
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self.tmin_valid = ( |
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-( |
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np.max([t1.max() - t1.min(), t2.max() - t2.min()]) |
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- np.min([t1.max() - t1.min(), t2.max() - t2.min()]) |
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) |
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/ 2 |
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+ self.t0_full |
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) |
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self.tmax_valid = ( |
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+( |
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np.max([t1.max() - t1.min(), t2.max() - t2.min()]) |
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- np.min([t1.max() - t1.min(), t2.max() - t2.min()]) |
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) |
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/ 2 |
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+ self.t0_full |
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) |
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def peak_find(self, smooth=False, smooth_std=None, Ninterp=1000): |
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"""Find the peaks of the correlation, optionally smoothing with a kernel of standard deviation `s`. |
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Returns dict with peak positions and significances, ordered from closest to farthest from zero. |
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""" |
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x, y = self.times, self.values |
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if smooth_std is None: |
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dt1 = np.mean(self.signal1.times[1:]-self.signal1.times[:-1]) |
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std1 = np.std(self.signal1.times[1:]-self.signal1.times[:-1]) |
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dt2 = np.mean(self.signal2.times[1:]-self.signal2.times[:-1]) |
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std2 = np.std(self.signal2.times[1:]-self.signal2.times[:-1]) |
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smooth_std = 1*np.max([dt1,dt2]) |
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if smooth: |
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xs, ys = interp_smooth_curve(x, y, smooth_std, Ninterp) |
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else: |
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xs, ys = x, y |
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idx, props = sp.signal.find_peaks(ys) |
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if smooth: |
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s1s_x, s1s_y = interp_smooth_curve(x, self.l1s[1], smooth_std, Ninterp) |
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else: |
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s1s_x, s1s_y = x, self.l1s[1] |
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peak_idx = idx[np.argsort(np.abs(xs[idx]))] |
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peak_x = xs[peak_idx] |
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peak_y = ys[peak_idx] |
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peak_signf1s = ys[peak_idx]/s1s_y[peak_idx] |
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peak_signif_percent = list() |
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for i in range(len(peak_x)): |
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f = sp.interpolate.interp1d(self.times, self.mc_corr, axis=-1) |
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peak_signif_percent.append( sp.stats.percentileofscore(f(peak_x[i]), peak_y[i], kind='strict') ) |
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return {'x':peak_x, 's':smooth_std, 'y':peak_y, 'signf1s':peak_signf1s, 'signif_percent':np.array(peak_signif_percent)} |
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def gen_synth(self, samples): |
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"""Generates the synthetic light curves. |
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Generates the specified number `samples` of synthetic light |
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curves for each signal, to be used to compute the significance |
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the correlation. |
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Parameters |
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---------- |
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samples : :py:class:`~int` |
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Number of synthetic light curves to be generated for each signal. |
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""" |
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self.samples = samples |
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self.signal1.gen_synth(samples) |
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self.signal2.gen_synth(samples) |
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def gen_corr(self, uncert=True, dsamples=500): |
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"""Generates the correlation of the signals. |
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Generates the correlation of the signals, and computes their |
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confidence level from the synthetic light curves, which must |
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have been generated before. |
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""" |
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if uncert and self.signal1.dvalues is None: |
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log.error( |
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"uncert is True but no uncertainties for Signal 1 were specified, setting uncert to False" |
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) |
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uncert = False |
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if uncert and self.signal2.dvalues is None: |
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log.error( |
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"uncert is True but no uncertainties for Signal 2 were specified, setting uncert to False" |
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) |
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uncert = False |
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if len(self.times) == 0 or len(self.dts) == 0: |
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raise Exception( |
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"You need to define the times on which to calculate the correlation." |
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"Please use gen_times() or manually set them." |
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) |
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# TODO: refactor if/elif with a helper function |
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mc_corr = np.empty((self.samples, self.times.size)) |
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if uncert: |
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mc_sig = np.empty((dsamples, self.times.size)) |
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if self.fcorr == "welsh": |
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for idx in range(self.samples): |
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mc_corr[idx] = welsh( |
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self.signal1.times, |
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self.signal1.synth[idx], |
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self.signal2.times, |
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self.signal2.synth[idx], |
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self.times, |
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self.dts, |
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) |
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if uncert: |
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for idx in range(dsamples): |
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mc_sig[idx] = welsh( |
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self.signal1.times, |
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self.signal1.values |
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+ self.signal1.dvalues * np.random.randn(self.signal1.values.size), |
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self.signal2.times, |
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self.signal2.values |
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+ self.signal2.dvalues * np.random.randn(self.signal2.values.size), |
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self.times, |
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self.dts, |
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) |
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self.values = welsh( |
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self.signal1.times, |
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self.signal1.values, |
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self.signal2.times, |
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self.signal2.values, |
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self.times, |
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self.dts, |
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) |
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elif self.fcorr == "kroedel": |
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for idx in range(self.samples): |
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mc_corr[idx] = kroedel( |
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self.signal1.times, |
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self.signal1.synth[idx], |
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self.signal2.times, |
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self.signal2.synth[idx], |
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self.times, |
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self.dts, |
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) |
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if uncert: |
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for idx in range(dsamples): |
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mc_sig[idx] = kroedel( |
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self.signal1.times, |
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self.signal1.values |
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+ self.signal1.dvalues * np.random.randn(self.signal1.values.size), |
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self.signal2.times, |
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self.signal2.values |
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+ self.signal2.dvalues * np.random.randn(self.signal2.values.size), |
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self.times, |
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self.dts, |
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) |
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self.values = kroedel( |
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self.signal1.times, |
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self.signal1.values, |
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self.signal2.times, |
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self.signal2.values, |
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self.times, |
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self.dts, |
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) |
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elif self.fcorr == "welsh_old": # should produce the exactly same results, but we keep it for debugs and testcov |
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for idx in range(self.samples): |
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mc_corr[idx] = welsh_old( |
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self.signal1.times, |
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self.signal1.synth[idx], |
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self.signal2.times, |
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self.signal2.synth[idx], |
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self.times, |
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self.dts, |
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) |
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if uncert: |
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for idx in range(dsamples): |
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mc_sig[idx] = welsh_old( |
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self.signal1.times, |
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self.signal1.values |
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+ self.signal1.dvalues * np.random.randn(self.signal1.values.size), |
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self.signal2.times, |
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self.signal2.values |
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+ self.signal2.dvalues * np.random.randn(self.signal2.values.size), |
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self.times, |
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self.dts, |
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) |
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self.values = welsh_old( |
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self.signal1.times, |
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self.signal1.values, |
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self.signal2.times, |
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self.signal2.values, |
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self.times, |
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self.dts, |
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) |
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elif self.fcorr == "kroedel_old": # should produce the exactly same results, but we keep it for debugs and testcov |
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for idx in range(self.samples): |
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mc_corr[idx] = kroedel_old( |
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self.signal1.times, |
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self.signal1.synth[idx], |
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self.signal2.times, |
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self.signal2.synth[idx], |
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self.times, |
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self.dts, |
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) |
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if uncert: |
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for idx in range(dsamples): |
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mc_sig[idx] = kroedel_old( |
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self.signal1.times, |
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self.signal1.values |
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+ self.signal1.dvalues * np.random.randn(self.signal1.values.size), |
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self.signal2.times, |
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self.signal2.values |
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+ self.signal2.dvalues * np.random.randn(self.signal2.values.size), |
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self.times, |
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self.dts, |
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) |
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self.values = kroedel_old( |
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self.signal1.times, |
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self.signal1.values, |
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self.signal2.times, |
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self.signal2.values, |
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self.times, |
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self.dts, |
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) |
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elif self.fcorr == "numpy": |
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for idx in range(self.samples): |
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mc_corr[idx] = nindcf( |
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self.signal1.times, |
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self.signal1.synth[idx], |
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self.signal2.times, |
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self.signal2.synth[idx], |
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) |
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if uncert: |
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for idx in range(dsamples): |
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mc_sig[idx] = nindcf( |
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self.signal1.times, |
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self.signal1.values |
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+ self.signal1.dvalues * np.random.randn(self.signal1.values.size), |
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self.signal2.times, |
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self.signal2.values |
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+ self.signal2.dvalues * np.random.randn(self.signal2.values.size), |
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) |
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self.values = nindcf( |
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self.signal1.times, |
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self.signal1.values, |
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self.signal2.times, |
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self.signal2.values, |
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) |
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else: |
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raise Exception("Unknown method " + self.fcorr + " for correlation.") |
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self.l3s = np.percentile(mc_corr, [0.135, 99.865], axis=0) |
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self.l2s = np.percentile(mc_corr, [2.28, 97.73], axis=0) |
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self.l1s = np.percentile(mc_corr, [15.865, 84.135], axis=0) |
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self.mc_corr = mc_corr # save them to be able to compute exact significance later... |
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if uncert: |
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self.s3s = np.percentile(mc_sig, [0.135, 99.865], axis=0) |
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self.s2s = np.percentile(mc_sig, [2.28, 97.73], axis=0) |
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self.s1s = np.percentile(mc_sig, [15.865, 84.135], axis=0) |
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def gen_times(self, ftimes="canopy", *args, **kwargs): |
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"""Sets times and bins using the method defined by ftimes parameter. |
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Parameters |
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---------- |
326
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ftimes : :py:class:`~str` |
327
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Method used to bin the time interval of the correlation. |
328
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Possible values are: |
329
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- "canopy": Computes a binning as dense as possible, with |
330
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variable bin width and (with a minimum and a maximum |
331
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resolution) and a minimum statistic. |
332
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- "rawab": Computes a binning with variable bin width, |
333
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a given step, maximum bin size and a minimum statistic. |
334
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- "uniform": Computes a binning with uniform bin width |
335
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and a minimum statistic. |
336
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- "numpy": Computes a binning suitable for method='numpy'. |
337
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""" |
338
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if ftimes == "canopy": |
339
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self.times, self.dts, self.nb = gen_times_canopy( |
340
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self.signal1.times, self.signal2.times, *args, **kwargs |
341
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) |
342
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elif ftimes == "rawab": |
343
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self.times, self.dts, self.nb = gen_times_rawab( |
344
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self.signal1.times, self.signal2.times, *args, **kwargs |
345
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) |
346
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elif ftimes == "uniform": |
347
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self.times, self.dts, self.nb = gen_times_uniform( |
348
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self.signal1.times, self.signal2.times, *args, **kwargs |
349
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) |
350
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elif ftimes == "numpy": |
351
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t1, t2 = self.signal1.times, self.signal1.times |
|
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|
352
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dt = np.max([(t1.max() - t1.min()) / t1.size, (t2.max() - t2.min()) / t2.size]) |
|
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|
353
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n1 = int(np.ptp(t1) / dt * 10.0) |
|
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|
354
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n2 = int(np.ptp(t1) / dt * 10.0) |
|
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|
355
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self.times = np.linspace(self.tmin_full, self.tmax_full, n1 + n2 - 1) |
356
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self.dts = np.full(self.times.size, (self.tmax_full - self.tmin_full) / (n1 + n2)) |
357
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else: |
358
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raise Exception("Unknown method " + ftimes + ", please indicate how to generate times.") |
359
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|
360
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def plot_corr(self, uncert=True, ax=None, legend=False): |
|
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|
361
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"""Plots the correlation of the signals. |
362
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|
363
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|
Plots the correlation of the signal, and the confidence limits |
364
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|
|
computed from the synthetic curves. |
365
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|
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|
366
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Parameters |
367
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---------- |
368
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ax : :class:`matplotlib.axes.Axes` |
369
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Axes to be used (default None, it creates a new axes). |
370
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legend : :py:class:`~bool` |
371
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|
Whether to add a legend indicating the confidence levels. |
372
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|
|
""" |
373
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|
374
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|
# TODO: develop a plotting object for plots |
|
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|
375
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# this will considerably shorten the |
376
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# number of attributes of this class |
377
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|
378
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if uncert and self.signal1.dvalues is None: |
379
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log.error( |
380
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"uncert is True but no uncertainties for Signal 1 were specified, setting uncert to False" |
|
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|
381
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|
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) |
382
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|
|
uncert = False |
383
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|
|
if uncert and self.signal2.dvalues is None: |
384
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|
|
log.error( |
385
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|
|
"uncert is True but no uncertainties for Signal 2 were specified, setting uncert to False" |
|
|
|
|
386
|
|
|
) |
387
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|
|
uncert = False |
388
|
|
|
|
389
|
|
|
# plt.figure() |
390
|
|
|
if ax is None: |
391
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|
|
ax = plt.gca() |
392
|
|
|
|
393
|
|
|
ax.plot(self.times, self.l1s[0], "c-.") |
394
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|
|
ax.plot(self.times, self.l1s[1], "c-.", label=r"$1\sigma$") |
395
|
|
|
ax.plot(self.times, self.l2s[0], "k--") |
396
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|
|
ax.plot(self.times, self.l2s[1], "k--", label=r"$2\sigma$") |
397
|
|
|
ax.plot(self.times, self.l3s[0], "r-") |
398
|
|
|
ax.plot(self.times, self.l3s[1], "r-", label=r"$3\sigma$") |
399
|
|
|
ax.plot(self.times, self.values, "b.--", lw=1) |
400
|
|
|
|
401
|
|
|
# full limit |
402
|
|
|
ax.axvline(x=self.tmin_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
403
|
|
|
ax.axvline(x=self.tmax_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
404
|
|
|
# same limit |
405
|
|
|
ax.axvline(x=self.tmin_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
406
|
|
|
ax.axvline(x=self.tmax_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
407
|
|
|
# valid limit |
408
|
|
|
ax.axvline(x=self.tmin_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
409
|
|
|
ax.axvline(x=self.tmax_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
410
|
|
|
|
411
|
|
|
if uncert: |
412
|
|
|
ax.fill_between(x=self.times, y1=self.s1s[0], y2=self.s1s[1], color="b", alpha=0.5) |
413
|
|
|
ax.fill_between(x=self.times, y1=self.s2s[0], y2=self.s2s[1], color="b", alpha=0.3) |
414
|
|
|
ax.fill_between(x=self.times, y1=self.s3s[0], y2=self.s3s[1], color="b", alpha=0.1) |
415
|
|
|
|
|
|
|
|
416
|
|
|
|
|
|
|
|
417
|
|
|
if legend: |
418
|
|
|
ax.legend() |
419
|
|
|
|
420
|
|
|
# plt.show() |
421
|
|
|
return ax |
422
|
|
|
|
423
|
|
|
def plot_times(self, rug=False): |
424
|
|
|
"""Plots the time binning generated previously. |
425
|
|
|
|
426
|
|
|
Plots the number of total bins, their distribution and the |
427
|
|
|
number of points in each bin for the generated time binning, |
428
|
|
|
previously generated with Correlation().gen_times(...). |
429
|
|
|
|
430
|
|
|
Parameters |
431
|
|
|
---------- |
432
|
|
|
rug : :py:class:`~bool` |
433
|
|
|
Whether to make a rug plot just below the binning, to make |
434
|
|
|
it easier to visually understand the density and distribution |
435
|
|
|
of the generated bins. |
436
|
|
|
|
437
|
|
|
""" |
438
|
|
|
|
439
|
|
|
# TODO: develop a plotting object for plots |
|
|
|
|
440
|
|
|
# this will considerably shorten the |
441
|
|
|
# number of attributes of this class |
442
|
|
|
|
443
|
|
|
fig, ax = plt.subplots(nrows=2, ncols=1, sharex=True) |
|
|
|
|
444
|
|
|
tab, dtab, nab = self.times, self.dts, self.nb |
445
|
|
|
|
446
|
|
|
fig.suptitle("Total bins: {:d}".format(self.times.size)) |
447
|
|
|
ax[0].plot(tab, nab, "b.") |
448
|
|
|
ax[0].errorbar(x=tab, y=nab, xerr=dtab / 2, fmt="none") |
449
|
|
|
ax[0].set_ylabel("$n_i$") |
450
|
|
|
ax[0].grid() |
451
|
|
|
ax[0].axvline(x=self.tmin_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
452
|
|
|
ax[0].axvline(x=self.tmax_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
453
|
|
|
ax[0].axvline(x=self.tmin_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
454
|
|
|
ax[0].axvline(x=self.tmax_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
455
|
|
|
ax[0].axvline(x=self.tmin_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
456
|
|
|
ax[0].axvline(x=self.tmax_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
457
|
|
|
ax[1].plot(tab, dtab, "b.") |
458
|
|
|
ax[1].set_ylabel("$dt_i$") |
459
|
|
|
# ax[1].grid() |
460
|
|
|
ax[1].axvline(x=self.tmin_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
461
|
|
|
ax[1].axvline(x=self.tmax_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
462
|
|
|
ax[1].axvline(x=self.tmin_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
463
|
|
|
ax[1].axvline(x=self.tmax_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
464
|
|
|
ax[1].axvline(x=self.tmin_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
465
|
|
|
ax[1].axvline(x=self.tmax_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
466
|
|
|
|
467
|
|
|
if rug: |
468
|
|
|
for time in self.times: |
469
|
|
|
ax[1].axvline(x=time, ymin=0, ymax=0.2, color="black", linewidth=0.8, alpha=1.0) |
470
|
|
|
# ax[1].plot(self.t, ax[1].get_ylim()[0]+np.zeros(self.t.size), 'k|', alpha=0.8, lw=1) |
471
|
|
|
|
472
|
|
|
ax[1].grid() |
473
|
|
|
# fig.show() |
474
|
|
|
|
475
|
|
|
def plot_signals(self, ax=None): |
|
|
|
|
476
|
|
|
"""Plots the signals involved in this correlation. |
477
|
|
|
|
478
|
|
|
Plots the signals involved in this correlation, in the same window |
479
|
|
|
but with different twin y-axes and different colors. |
480
|
|
|
|
481
|
|
|
Parameters |
482
|
|
|
---------- |
483
|
|
|
ax : :py:class:`~matplotlib.axes.Axes` |
484
|
|
|
Axes to be used for plotting. |
485
|
|
|
""" |
486
|
|
|
|
487
|
|
|
# TODO: develop a plotting object for plots |
|
|
|
|
488
|
|
|
# this will considerably shorten the |
489
|
|
|
# number of attributes of this class |
490
|
|
|
|
491
|
|
|
if ax is None: |
492
|
|
|
ax = plt.gca() |
493
|
|
|
|
494
|
|
|
ax.plot(self.signal1.times, self.signal1.values, "b.-", lw=1, alpha=0.4) |
495
|
|
|
ax.tick_params(axis="y", labelcolor="b") |
496
|
|
|
ax.set_ylabel("sig 1", color="b") |
497
|
|
|
|
498
|
|
|
ax2 = ax.twinx() |
499
|
|
|
ax2.plot(self.signal2.times, self.signal2.values, "r.-", lw=1, alpha=0.4) |
500
|
|
|
ax2.tick_params(axis="y", labelcolor="r") |
501
|
|
|
ax2.set_ylabel("sig 2", color="r") |
502
|
|
|
|