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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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__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, k=3, a=-0.1, b=0.1, n=5, ax=None): |
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"""Find the peak of the correlation |
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""" |
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x, y = self.times, self.values |
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t = np.linspace(a, b, n) |
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spl = sp.interpolate.LSQUnivariateSpline(x, y, t, k=3) |
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xs = np.linspace(min(x), max(x), 1000) |
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ys = spl(xs) |
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peak_idx = np.argmax(ys) |
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peak_x = xs[peak_idx] |
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peak_y = ys[peak_idx] |
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if ax is None: |
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print(f'Peak at {365*peak_x:.1f} days (C = {peak_y:.2f})') |
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fig, ax = plt.subplots() |
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self.plot_corr() |
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plt.xlim([-100/365,100/365]) |
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plt.plot(xs, ys, 'k-') |
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#plot_corr_set_axs() |
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return {'x_peak':peak_x, 'y_peak':peak_y} |
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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_ab": |
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for idx in range(self.samples): |
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mc_corr[idx] = welsh_ab( |
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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_ab( |
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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_ab( |
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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_ab": |
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for idx in range(self.samples): |
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mc_corr[idx] = kroedel_ab( |
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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_ab( |
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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_ab( |
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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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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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---------- |
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ftimes : :py:class:`~str` |
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Method used to bin the time interval of the correlation. |
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Possible values are: |
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- "canopy": Computes a binning as dense as possible, with |
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variable bin width and (with a minimum and a maximum |
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resolution) and a minimum statistic. |
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- "rawab": Computes a binning with variable bin width, |
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a given step, maximum bin size and a minimum statistic. |
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- "uniform": Computes a binning with uniform bin width |
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and a minimum statistic. |
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- "numpy": Computes a binning suitable for method='numpy'. |
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""" |
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if ftimes == "canopy": |
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self.times, self.dts, self.nb = gen_times_canopy( |
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self.signal1.times, self.signal2.times, *args, **kwargs |
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) |
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elif ftimes == "rawab": |
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self.times, self.dts, self.nb = gen_times_rawab( |
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self.signal1.times, self.signal2.times, *args, **kwargs |
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) |
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elif ftimes == "uniform": |
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self.times, self.dts, self.nb = gen_times_uniform( |
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self.signal1.times, self.signal2.times, *args, **kwargs |
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) |
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elif ftimes == "numpy": |
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t1, t2 = self.signal1.times, self.signal1.times |
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dt = np.max([(t1.max() - t1.min()) / t1.size, (t2.max() - t2.min()) / t2.size]) |
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n1 = int(np.ptp(t1) / dt * 10.0) |
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n2 = int(np.ptp(t1) / dt * 10.0) |
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self.times = np.linspace(self.tmin_full, self.tmax_full, n1 + n2 - 1) |
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self.dts = np.full(self.times.size, (self.tmax_full - self.tmin_full) / (n1 + n2)) |
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else: |
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raise Exception("Unknown method " + ftimes + ", please indicate how to generate times.") |
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def plot_corr(self, uncert=True, peak=False, ax=None, legend=False): |
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"""Plots the correlation of the signals. |
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288
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Plots the correlation of the signal, and the confidence limits |
|
289
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|
computed from the synthetic curves. |
|
290
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|
|
291
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|
|
Parameters |
|
292
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|
|
---------- |
|
293
|
|
|
ax : :class:`matplotlib.axes.Axes` |
|
294
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|
|
Axes to be used (default None, it creates a new axes). |
|
295
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|
legend : :py:class:`~bool` |
|
296
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|
|
Whether to add a legend indicating the confidence levels. |
|
297
|
|
|
""" |
|
298
|
|
|
|
|
299
|
|
|
# TODO: develop a plotting object for plots |
|
|
|
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|
|
300
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# this will considerably shorten the |
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301
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# number of attributes of this class |
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302
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|
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303
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if uncert and self.signal1.dvalues is None: |
|
304
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log.error( |
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305
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"uncert is True but no uncertainties for Signal 1 were specified, setting uncert to False" |
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|
|
|
|
|
306
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) |
|
307
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uncert = False |
|
308
|
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if uncert and self.signal2.dvalues is None: |
|
309
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|
log.error( |
|
310
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|
"uncert is True but no uncertainties for Signal 2 were specified, setting uncert to False" |
|
|
|
|
|
|
311
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|
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) |
|
312
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|
uncert = False |
|
313
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|
|
314
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|
# plt.figure() |
|
315
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if ax is None: |
|
316
|
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ax = plt.gca() |
|
317
|
|
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|
|
318
|
|
|
ax.plot(self.times, self.l1s[0], "c-.") |
|
319
|
|
|
ax.plot(self.times, self.l1s[1], "c-.", label=r"$1\sigma$") |
|
320
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|
|
ax.plot(self.times, self.l2s[0], "k--") |
|
321
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|
|
ax.plot(self.times, self.l2s[1], "k--", label=r"$2\sigma$") |
|
322
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|
|
ax.plot(self.times, self.l3s[0], "r-") |
|
323
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|
|
ax.plot(self.times, self.l3s[1], "r-", label=r"$3\sigma$") |
|
324
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|
ax.plot(self.times, self.values, "b.--", lw=1) |
|
325
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|
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|
|
326
|
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|
# full limit |
|
327
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|
|
ax.axvline(x=self.tmin_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
|
328
|
|
|
ax.axvline(x=self.tmax_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
|
329
|
|
|
# same limit |
|
330
|
|
|
ax.axvline(x=self.tmin_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
|
331
|
|
|
ax.axvline(x=self.tmax_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
|
332
|
|
|
# valid limit |
|
333
|
|
|
ax.axvline(x=self.tmin_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
|
334
|
|
|
ax.axvline(x=self.tmax_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
|
335
|
|
|
|
|
336
|
|
|
if uncert: |
|
337
|
|
|
ax.fill_between(x=self.times, y1=self.s1s[0], y2=self.s1s[1], color="b", alpha=0.5) |
|
338
|
|
|
ax.fill_between(x=self.times, y1=self.s2s[0], y2=self.s2s[1], color="b", alpha=0.3) |
|
339
|
|
|
ax.fill_between(x=self.times, y1=self.s3s[0], y2=self.s3s[1], color="b", alpha=0.1) |
|
340
|
|
|
|
|
341
|
|
|
if peak: |
|
342
|
|
|
peak_sp = self.peak_find(ax=ax) |
|
343
|
|
|
ax.annotate(f"Peak at ({365*peak_sp['x_peak']:.1f}, {peak_sp['y_peak']:.2f})", (peak_sp['x_peak'], peak_sp['y_peak'])) |
|
|
|
|
|
|
344
|
|
|
|
|
|
|
|
|
|
345
|
|
|
|
|
|
|
|
|
|
346
|
|
|
if legend: |
|
347
|
|
|
ax.legend() |
|
348
|
|
|
|
|
349
|
|
|
# plt.show() |
|
350
|
|
|
return ax |
|
351
|
|
|
|
|
352
|
|
|
def plot_times(self, rug=False): |
|
353
|
|
|
"""Plots the time binning generated previously. |
|
354
|
|
|
|
|
355
|
|
|
Plots the number of total bins, their distribution and the |
|
356
|
|
|
number of points in each bin for the generated time binning, |
|
357
|
|
|
previously generated with Correlation().gen_times(...). |
|
358
|
|
|
|
|
359
|
|
|
Parameters |
|
360
|
|
|
---------- |
|
361
|
|
|
rug : :py:class:`~bool` |
|
362
|
|
|
Whether to make a rug plot just below the binning, to make |
|
363
|
|
|
it easier to visually understand the density and distribution |
|
364
|
|
|
of the generated bins. |
|
365
|
|
|
|
|
366
|
|
|
""" |
|
367
|
|
|
|
|
368
|
|
|
# TODO: develop a plotting object for plots |
|
|
|
|
|
|
369
|
|
|
# this will considerably shorten the |
|
370
|
|
|
# number of attributes of this class |
|
371
|
|
|
|
|
372
|
|
|
fig, ax = plt.subplots(nrows=2, ncols=1, sharex=True) |
|
|
|
|
|
|
373
|
|
|
tab, dtab, nab = self.times, self.dts, self.nb |
|
374
|
|
|
|
|
375
|
|
|
fig.suptitle("Total bins: {:d}".format(self.times.size)) |
|
376
|
|
|
ax[0].plot(tab, nab, "b.") |
|
377
|
|
|
ax[0].errorbar(x=tab, y=nab, xerr=dtab / 2, fmt="none") |
|
378
|
|
|
ax[0].set_ylabel("$n_i$") |
|
379
|
|
|
ax[0].grid() |
|
380
|
|
|
ax[0].axvline(x=self.tmin_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
|
381
|
|
|
ax[0].axvline(x=self.tmax_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
|
382
|
|
|
ax[0].axvline(x=self.tmin_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
|
383
|
|
|
ax[0].axvline(x=self.tmax_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
|
384
|
|
|
ax[0].axvline(x=self.tmin_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
|
385
|
|
|
ax[0].axvline(x=self.tmax_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
|
386
|
|
|
ax[1].plot(tab, dtab, "b.") |
|
387
|
|
|
ax[1].set_ylabel("$dt_i$") |
|
388
|
|
|
# ax[1].grid() |
|
389
|
|
|
ax[1].axvline(x=self.tmin_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
|
390
|
|
|
ax[1].axvline(x=self.tmax_full, ymin=-1, ymax=+1, color="red", linewidth=4, alpha=0.5) |
|
391
|
|
|
ax[1].axvline(x=self.tmin_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
|
392
|
|
|
ax[1].axvline(x=self.tmax_same, ymin=-1, ymax=+1, color="black", linewidth=2, alpha=0.5) |
|
393
|
|
|
ax[1].axvline(x=self.tmin_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
|
394
|
|
|
ax[1].axvline(x=self.tmax_valid, ymin=-1, ymax=+1, color="cyan", linewidth=1, alpha=0.5) |
|
395
|
|
|
|
|
396
|
|
|
if rug: |
|
397
|
|
|
for time in self.times: |
|
398
|
|
|
ax[1].axvline(x=time, ymin=0, ymax=0.2, color="black", linewidth=0.8, alpha=1.0) |
|
399
|
|
|
# ax[1].plot(self.t, ax[1].get_ylim()[0]+np.zeros(self.t.size), 'k|', alpha=0.8, lw=1) |
|
400
|
|
|
|
|
401
|
|
|
ax[1].grid() |
|
402
|
|
|
# fig.show() |
|
403
|
|
|
|
|
404
|
|
|
def plot_signals(self, ax=None): |
|
|
|
|
|
|
405
|
|
|
"""Plots the signals involved in this correlation. |
|
406
|
|
|
|
|
407
|
|
|
Plots the signals involved in this correlation, in the same window |
|
408
|
|
|
but with different twin y-axes and different colors. |
|
409
|
|
|
|
|
410
|
|
|
Parameters |
|
411
|
|
|
---------- |
|
412
|
|
|
ax : :py:class:`~matplotlib.axes.Axes` |
|
413
|
|
|
Axes to be used for plotting. |
|
414
|
|
|
""" |
|
415
|
|
|
|
|
416
|
|
|
# TODO: develop a plotting object for plots |
|
|
|
|
|
|
417
|
|
|
# this will considerably shorten the |
|
418
|
|
|
# number of attributes of this class |
|
419
|
|
|
|
|
420
|
|
|
if ax is None: |
|
421
|
|
|
ax = plt.gca() |
|
422
|
|
|
|
|
423
|
|
|
ax.plot(self.signal1.times, self.signal1.values, "b.-", lw=1, alpha=0.4) |
|
424
|
|
|
ax.tick_params(axis="y", labelcolor="b") |
|
425
|
|
|
ax.set_ylabel("sig 1", color="b") |
|
426
|
|
|
|
|
427
|
|
|
ax2 = ax.twinx() |
|
428
|
|
|
ax2.plot(self.signal2.times, self.signal2.values, "r.-", lw=1, alpha=0.4) |
|
429
|
|
|
ax2.tick_params(axis="y", labelcolor="r") |
|
430
|
|
|
ax2.set_ylabel("sig 2", color="r") |
|
431
|
|
|
|
IAA-CSIC /
MUTIS
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