Source code for gammapy.time.lightcurve

# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
from collections import OrderedDict
import numpy as np
import astropy.units as u
from astropy.table import Table
from astropy.time import Time
from ..spectrum.utils import CountsPredictor
from ..stats.poisson import excess_error, excess_ul_helene
from ..utils.scripts import make_path
from ..utils.table import table_from_row_data
from ..stats.poisson import significance_on_off

__all__ = ["LightCurve", "LightCurveEstimator"]


[docs]class LightCurve(object): """Lightcurve container. The lightcurve data is stored in ``table``. For now we only support times stored in MJD format! TODO: specification of format is work in progress See https://github.com/open-gamma-ray-astro/gamma-astro-data-formats/pull/61 Usage: :ref:`time-lc` Parameters ---------- table : `~astropy.table.Table` Table with lightcurve data """ def __init__(self, table): self.table = table def __repr__(self): return "{}(len={})".format(self.__class__.__name__, len(self.table)) @property def time_scale(self): """Time scale (str). Taken from table "TIMESYS" header. Common values: "TT" or "UTC". Assumed default is "UTC". """ return self.table.meta.get("TIMESYS", "utc") @property def time_format(self): """Time format (str).""" return "mjd" # @property # def time_ref(self): # """Time reference (`~astropy.time.Time`).""" # return time_ref_from_dict(self.table.meta) def _make_time(self, colname): val = self.table[colname].data scale = self.time_scale format = self.time_format return Time(val, scale=scale, format=format) @property def time(self): """Time (`~astropy.time.Time`).""" return self._make_time("time") @property def time_min(self): """Time bin start (`~astropy.time.Time`).""" return self._make_time("time_min") @property def time_max(self): """Time bin end (`~astropy.time.Time`).""" return self._make_time("time_max") @property def time_mid(self): """Time bin center (`~astropy.time.Time`).""" return self.time_min + 0.5 * self.time_delta @property def time_delta(self): """Time bin width (`~astropy.time.TimeDelta`).""" return self.time_max - self.time_min
[docs] @classmethod def read(cls, filename, **kwargs): """Read from file. Parameters ---------- filename : str Filename kwargs : dict Keyword arguments passed to `astropy.table.Table.read`. """ filename = make_path(filename) table = Table.read(str(filename), **kwargs) return cls(table=table)
[docs] def write(self, filename, **kwargs): """Write to file. Parameters ---------- filename : str Filename kwargs : dict Keyword arguments passed to `astropy.table.Table.write`. """ filename = make_path(filename) self.table.write(str(filename), **kwargs)
[docs] def compute_fvar(self): r"""Calculate the fractional excess variance. This method accesses the the ``FLUX`` and ``FLUX_ERR`` columns from the lightcurve data. The fractional excess variance :math:`F_{var}`, an intrinsic variability estimator, is given by .. math:: F_{var} = \sqrt{\frac{S^{2} - \bar{\sigma^{2}}}{\bar{x}^{2}}}. It is the excess variance after accounting for the measurement errors on the light curve :math:`\sigma`. :math:`S` is the variance. Returns ------- fvar, fvar_err : `~numpy.ndarray` Fractional excess variance. References ---------- .. [Vaughan2003] "On characterizing the variability properties of X-ray light curves from active galaxies", Vaughan et al. (2003) http://adsabs.harvard.edu/abs/2003MNRAS.345.1271V """ flux = self.table["flux"].data.astype("float64") flux_err = self.table["flux_err"].data.astype("float64") flux_mean = np.mean(flux) n_points = len(flux) s_square = np.sum((flux - flux_mean) ** 2) / (n_points - 1) sig_square = np.nansum(flux_err ** 2) / n_points fvar = np.sqrt(np.abs(s_square - sig_square)) / flux_mean sigxserr_a = np.sqrt(2 / n_points) * (sig_square / flux_mean) ** 2 sigxserr_b = np.sqrt(sig_square / n_points) * (2 * fvar / flux_mean) sigxserr = np.sqrt(sigxserr_a ** 2 + sigxserr_b ** 2) fvar_err = sigxserr / (2 * fvar) return fvar, fvar_err
[docs] def compute_chisq(self): """Calculate the chi-square test for `LightCurve`. Chisquare test is a variability estimator. It computes deviations from the expected value here mean value Returns ------- ChiSq, P-value : tuple of float or `~numpy.ndarray` Tuple of Chi-square and P-value """ import scipy.stats as stats flux = self.table["flux"] yexp = np.mean(flux) yobs = flux.data chi2, pval = stats.chisquare(yobs, yexp) return chi2, pval
[docs] def plot(self, ax=None, time_format="mjd", flux_unit="cm-2 s-1", **kwargs): """Plot flux points. Parameters ---------- ax : `~matplotlib.axes.Axes`, optional. The `~matplotlib.axes.Axes` object to be drawn on. If None, uses the current `~matplotlib.axes.Axes`. time_format : {'mjd', 'iso'}, optional If 'iso', the x axis will contain Matplotlib dates. For formatting these dates see: https://matplotlib.org/gallery/ticks_and_spines/date_demo_rrule.html flux_unit : str, `~astropy.units.Unit`, optional Unit of the flux axis kwargs : dict Keyword arguments passed to :func:`matplotlib.pyplot.errorbar` Returns ------- ax : `~matplotlib.axes.Axes` Axis object """ import matplotlib.pyplot as plt from matplotlib.dates import DateFormatter if ax is None: ax = plt.gca() y, yerr = self._get_fluxes_and_errors(flux_unit) is_ul, yul = self._get_flux_uls(flux_unit) x, xerr = self._get_times_and_errors(time_format) # length of the ul arrow ul_arr = ( np.nanmax(np.concatenate((y[~is_ul], yul[is_ul]))) - np.nanmin(np.concatenate((y[~is_ul], yul[is_ul]))) ) * 0.1 # join fluxes and upper limits for the plot y[is_ul] = yul[is_ul] yerr[0][is_ul] = ul_arr # set plotting defaults and plot kwargs.setdefault("marker", "+") kwargs.setdefault("ls", "None") ax.errorbar(x=x, y=y, xerr=xerr, yerr=yerr, uplims=is_ul, **kwargs) ax.set_xlabel("Time ({})".format(time_format.upper())) ax.set_ylabel("Flux ({0:FITS})".format(u.Unit(flux_unit))) if time_format == "iso": ax.xaxis.set_major_formatter(DateFormatter("%Y-%m-%d %H:%M:%S")) plt.setp( ax.xaxis.get_majorticklabels(), rotation=30, ha="right", rotation_mode="anchor", ) return ax
def _get_fluxes_and_errors(self, unit="cm-2 s-1"): """Extract fluxes and corresponding errors Helper function for the plot method. Parameters ---------- unit : str, `~astropy.units.Unit`, optional Unit of the returned flux and errors values Returns ------- y : `numpy.ndarray` Flux values (yn, yp) : tuple of `numpy.ndarray` Flux error values """ y = self.table["flux"].quantity.to(unit) if all(k in self.table.colnames for k in ["flux_errp", "flux_errn"]): yp = self.table["flux_errp"].quantity.to(unit) yn = self.table["flux_errn"].quantity.to(unit) elif "flux_err" in self.table.colnames: yp = self.table["flux_err"].quantity.to(unit) yn = self.table["flux_err"].quantity.to(unit) else: yp, yn = np.zeros_like(y), np.zeros_like(y) return y.value, (yn.value, yp.value) def _get_flux_uls(self, unit="cm-2 s-1"): """Extract flux upper limits Helper function for the plot method. Parameters ---------- unit : str, `~astropy.units.Unit`, optional Unit of the returned flux upper limit values Returns ------- is_ul : `numpy.ndarray` Is flux point is an upper limit? (boolean array) yul : `numpy.ndarray` Flux upper limit values """ try: is_ul = self.table["is_ul"].data.astype("bool") except KeyError: is_ul = np.zeros_like(self.table["flux"]).data.astype("bool") if is_ul.any(): yul = self.table["flux_ul"].quantity.to(unit) else: yul = np.zeros_like(self.table["flux"]).quantity yul[:] = np.nan return is_ul, yul.value def _get_times_and_errors(self, time_format="mjd"): """Extract times and corresponding errors Helper function for the plot method. Parameters ---------- time_format : {'mjd', 'iso'}, optional Time format of the times. If 'iso', times and errors will be returned as `~datetime.datetime` and `~datetime.timedelta` objects Returns ------- x : `~numpy.ndarray` or of `~datetime.datetime` Time values or `~datetime.datetime` instances if 'iso' is chosen as time format (xn, xp) : tuple of `numpy.ndarray` of `~datetime.timedelta` Tuple of time error values or `~datetime.timedelta` instances if 'iso' is chosen as time format """ from matplotlib.dates import num2timedelta try: x = self.time except KeyError: x = self.time_mid try: xn, xp = x - self.time_min, self.time_max - x except KeyError: xn, xp = x - x, x - x # convert to given time format if time_format == "iso": x = x.datetime # TODO: In astropy version >3.1 the TimeDelta.to_datetime() method # should start working, for now i will use num2timedelta. xn = np.asarray(num2timedelta(xn.to("d").value)) xp = np.asarray(num2timedelta(xp.to("d").value)) elif time_format == "mjd": x = x.mjd xn, xp = xn.to("d").value, xp.to("d").value else: raise ValueError( "The time format '{}' is not supported.".format(time_format) ) return x, (xn, xp)
[docs]class LightCurveEstimator(object): """Light curve estimator. For a usage example see :gp-notebook:`light_curve`. Parameters ---------- spec_extract : `~gammapy.spectrum.SpectrumExtraction` Contains statistics, IRF and event lists """ def __init__(self, spec_extract): self.observations = spec_extract.observations self.obs_spec = spec_extract.spectrum_observations self.off_evt_list = self._get_off_evt_list(spec_extract) self.on_evt_list = self._get_on_evt_list(spec_extract) @staticmethod def _get_off_evt_list(spec_extract): """ Returns list of OFF events for each observations """ off_evt_list = [] for bg in spec_extract.bkg_estimate: off_evt_list.append(bg.off_events) return off_evt_list @staticmethod def _get_on_evt_list(spec_extract): """ Returns list of ON events for each observations """ on_evt_list = [] for obs in spec_extract.bkg_estimate: on_evt_list.append(obs.on_events) return on_evt_list
[docs] @staticmethod def make_time_intervals_fixes(time_step, spectrum_extraction): """Create time intervals of fixed size. Parameters ---------- time_step : float Size of the light curve bins in seconds spectrum_extraction : `~gammapy.spectrum.SpectrumExtraction` Contains statistics, IRF and event lists Returns ------- table : `~astropy.table.Table` Table of time intervals Examples -------- To extract intervals for light curve:: intervals = list(zip(table['t_start'], table['t_stop'])) """ rows = [] time_start = Time(100000, format="mjd") time_end = Time(0, format="mjd") time_step = time_step / (24 * 3600) for obs in spectrum_extraction.observations: time_events = obs.events.time if time_start > time_events.min(): time_start = time_events.min() if time_end < time_events.max(): time_end = time_events.max() time = time_start.value while time < time_end.value: time += time_step rows.append( dict( t_start=Time(time - time_step, format="mjd", scale="tt"), t_stop=Time(time, format="mjd", scale="tt"), ) ) return Table(rows=rows)
def _create_and_filter_onofflists( self, t_index, energy_range=None, interval=None, extra=False ): """Extract on and off events list from an observation and apply energy and time filters Helper function for compute_flux_point and make_time_intervals_min_significance Parameters ---------- t_index : int index in self of the observation to use energy_range : `~astropy.units.Quantity` True energy range to filter the events interval : `~astropy.time.Time` Time interval (2-element array) extra : boolean Define if we want spec and e_reco in output Returns ------- on : `~gammapy.data.EventList` List of on events off : `~gammapy.data.EventList` List of on events """ spec = self.obs_spec[t_index] # get ON and OFF evt list off = self.off_evt_list[t_index] on = self.on_evt_list[t_index] # introduce the e_reco binning here e_reco = spec.e_reco if energy_range is not None: emin = e_reco[e_reco.searchsorted(max(spec.lo_threshold, energy_range[0]))] emax = e_reco[ e_reco.searchsorted(min(spec.hi_threshold, energy_range[1])) - 1 ] # filter the event list with energy on = on.select_energy([emin, emax]) on = on.select_energy(energy_range) off = off.select_energy([emin, emax]) off = off.select_energy(energy_range) if interval is not None: # filter the event list with time tmin = interval[0] tmax = interval[1] on = on.select_time([tmin, tmax]) off = off.select_time([tmin, tmax]) if extra: return on, off, spec, e_reco return on, off @staticmethod def _alpha(time_holder, obs_properties, n, istart, i): """ Helper function for make_time_intervals_min_significance Parameters ---------- time_holder : list of float and flag Contains a list of a time and a flag in 2-element arrays obs_properties : `~astropy.table.Table` Contains the dead time fraction and ratio of the on/off region n : int First observation to use istart : int index of the first event of the interval i : int index of the last event of the interval """ def in_list(item, L): o, j = np.where(L == item) for index in o: yield index alpha = 0 tmp = 0 time = 0 xm1 = istart # loop over observations for x in in_list("end", time_holder[istart : i + 1]): if tmp == 0: alpha += ( (1 - obs_properties["deadtime"][n]) * ( float(time_holder[x][0]) - (float(time_holder[xm1][0]) + float(time_holder[xm1 - 1][0])) / 2 ) * obs_properties["A_off"][n + tmp] ) time += (1 - obs_properties["deadtime"][n]) * ( float(time_holder[x][0]) - (float(time_holder[xm1][0]) + float(time_holder[xm1 - 1][0])) / 2 ) xm1 = x + 1 tmp += 1 else: alpha += ( (1 - obs_properties["deadtime"][n + tmp]) * (float(time_holder[x][0]) - float(time_holder[xm1][0])) * obs_properties["A_off"][n + tmp] ) time += (1 - obs_properties["deadtime"][n + tmp]) * ( float(time_holder[x][0]) - float(time_holder[xm1][0]) ) xm1 = x + 1 tmp += 1 alpha += ( (1 - obs_properties["deadtime"][n + tmp]) * ( (float(time_holder[i][0]) + float(time_holder[i][0])) / 2 - float(time_holder[xm1][0]) ) * obs_properties["A_off"][n + tmp] ) time += (1 - obs_properties["deadtime"][n + tmp]) * ( (float(time_holder[i][0]) + float(time_holder[i][0])) / 2 - float(time_holder[xm1][0]) ) alpha = time / alpha return alpha
[docs] def make_time_intervals_min_significance( self, significance, significance_method, energy_range, spectrum_extraction, separators=None, ): """ Create time intervals such that each bin of a light curve reach a given significance The function work event by event to create an interval containing enough statistic and then starting a new one Parameters ---------- significance : float Target significance for each light curve point significance_method : {'lima', 'simple'} Significance method (see `~gammapy.stats.significance_on_off`) energy_range : `~astropy.units.Quantity` True energy range to evaluate integrated flux (true energy) spectrum_extraction : `~gammapy.spectrum.SpectrumExtraction` Contains statistics, IRF and event lists separators : list of `~astropy.time.Time` Contains a list of time to stop the current point creation (not saved) and start a new one Mostly useful between observations separated by a large time gap Returns ------- table : `~astropy.table.Table` Table of time intervals and information about their content : on/off events, alpha, significance Examples -------- extract intervals for light curve : intervals = list(zip(table['t_start'], table['t_stop'])) """ # The function create a list of time associated with identifiers called time_holder. # The identifiers can be 'on' for the on events, 'off' for the off events, 'start' for the start of an # observation, 'end for the end of an observation and 'break' for a separator. # The function then loop other all the elements of this list time_holder = [] obs_properties = [] n_obs = 0 # extract the separators if separators is not None: for time in separators: time_holder.append([time.tt.mjd, "break"]) # recovers the starting and ending time of each observations and useful properties for obs in spectrum_extraction.observations: time_holder.append([obs.events.observation_time_start.tt.mjd, "start"]) time_holder.append([obs.events.observation_time_end.tt.mjd, "end"]) obs_properties.append( dict( deadtime=obs.observation_dead_time_fraction, A_off=spectrum_extraction.bkg_estimate[n_obs].a_off, ) ) n_obs += 1 obs_properties = Table(rows=obs_properties) # prepare the on and off photon list as in the flux point computation -> should be updated accordingly for t_index, obs in enumerate(self.observations): on, off = self._create_and_filter_onofflists( t_index=t_index, energy_range=energy_range ) for time in on.time.tt.mjd: time_holder.append([time, "on"]) for time in off.time.tt.mjd: time_holder.append([time, "off"]) # sort all elements in the table by time time_holder = sorted(time_holder, key=lambda item: item[0]) time_holder = np.asarray(time_holder) rows = [] istart = 1 i = 1 n = 0 while time_holder[i][0] < time_holder[-1][0]: i += 1 if time_holder[i][1] == "break": while time_holder[i + 1][1] != "on" and time_holder[i + 1][1] != "off": i += 1 n += np.sum(time_holder[istart:i] == "end") istart = i continue if time_holder[i][1] != "on" and time_holder[i][1] != "off": continue # compute alpha alpha = self._alpha(time_holder, obs_properties, n, istart, i) non = np.sum(time_holder[istart : i + 1] == "on") noff = np.sum(time_holder[istart : i + 1] == "off") # check the significance signif = significance_on_off(non, noff, alpha, method=significance_method) if signif > significance: rows.append( dict( t_start=( float(time_holder[istart - 1][0]) + float(time_holder[istart][0]) ) / 2, t_stop=(float(time_holder[i][0]) + float(time_holder[i + 1][0])) / 2, n_on=non, n_off=noff, alpha=alpha, significance=signif, ) ) # start the next interval while ( time_holder[i + 1][0] < time_holder[-1][0] and time_holder[i + 1][1] != "on" and time_holder[i + 1][1] != "off" ): i += 1 n += np.sum(time_holder[istart : i + 1] == "end") istart = i + 1 i = istart table = Table(rows=rows) table["t_start"] = Time(table["t_start"], format="mjd", scale="tt") table["t_stop"] = Time(table["t_stop"], format="mjd", scale="tt") return table
[docs] def light_curve( self, time_intervals, spectral_model, energy_range, ul_significance=3 ): """Compute light curve. Implementation follows what is done in: http://adsabs.harvard.edu/abs/2010A%26A...520A..83H. To be discussed: assumption that threshold energy in the same in reco and true energy. Parameters ---------- time_intervals : list of `~astropy.time.Time` List of time intervals spectral_model : `~gammapy.spectrum.models.SpectralModel` Spectral model energy_range : `~astropy.units.Quantity` True energy range to evaluate integrated flux (true energy) ul_significance : float Upper limit confidence level significance Returns ------- lc : `~gammapy.time.LightCurve` Light curve """ rows = [] for time_interval in time_intervals: useinterval, row = self.compute_flux_point( time_interval, spectral_model, energy_range, ul_significance ) if useinterval: rows.append(row) table = table_from_row_data(rows) # TODO: check why stripping of the units here is needed table["time_min"] = table["time_min"].data table["time_max"] = table["time_max"].data return LightCurve(table)
[docs] def compute_flux_point( self, time_interval, spectral_model, energy_range, ul_significance=3 ): """Compute one flux point for one time interval. Parameters ---------- time_interval : `~astropy.time.Time` Time interval (2-element array, or a tuple of Time objects) spectral_model : `~gammapy.spectrum.models.SpectralModel` Spectral model energy_range : `~astropy.units.Quantity` True energy range to evaluate integrated flux (true energy) ul_significance : float Upper limit confidence level significance Returns ------- useinterval : bool Is True if the time_interval produce a valid flux point measurements : dict Dictionary with flux point measurement in the time interval """ tmin, tmax = time_interval[0], time_interval[1] livetime = 0 alpha_mean = 0.0 alpha_mean_backup = 0.0 measured_excess = 0 predicted_excess = 0 n_on = 0 n_off = 0 useinterval = False # Loop on observations for t_index, obs in enumerate(self.observations): # discard observations not matching the time interval obs_start = obs.events.observation_time_start obs_stop = obs.events.observation_time_end if (tmin < obs_start and tmax < obs_start) or (tmin > obs_stop): continue useinterval = True # get ON and OFF evt list on, off, spec, e_reco = self._create_and_filter_onofflists( t_index=t_index, energy_range=energy_range, interval=[tmin, tmax], extra=True, ) n_on_obs = len(on.table) n_off_obs = len(off.table) # compute effective livetime (for the interval) if tmin >= obs_start and tmax <= obs_stop: # interval included in obs livetime_to_add = (tmax - tmin).to("s") elif tmin >= obs_start and tmax >= obs_stop: # interval min above tstart from obs livetime_to_add = (obs_stop - tmin).to("s") elif tmin <= obs_start and tmax <= obs_stop: # interval min below tstart from obs livetime_to_add = (tmax - obs_start).to("s") elif tmin <= obs_start and tmax >= obs_stop: # obs included in interval livetime_to_add = (obs_stop - obs_start).to("s") else: livetime_to_add = u.Quantity(0, "s") # Take into account dead time livetime_to_add *= 1.0 - obs.observation_dead_time_fraction # Compute excess obs_measured_excess = n_on_obs - spec.alpha * n_off_obs # Compute the expected excess in the range given by the user # but must respect the energy threshold of the observation # (to match the energy range of the measured excess) # We use the effective livetime and the right energy threshold e_idx = np.where( np.logical_and.reduce( ( e_reco >= spec.lo_threshold, # threshold e_reco <= spec.hi_threshold, # threshold e_reco >= energy_range[0], # user e_reco <= energy_range[-1], ) # user ) )[0] counts_predictor = CountsPredictor( livetime=livetime_to_add, aeff=spec.aeff, edisp=spec.edisp, model=spectral_model, ) counts_predictor.run() counts_predicted_excess = counts_predictor.npred.data.data[e_idx[:-1]] obs_predicted_excess = np.sum(counts_predicted_excess) # compute effective normalisation between ON/OFF (for the interval) livetime += livetime_to_add alpha_mean += spec.alpha * n_off_obs alpha_mean_backup += spec.alpha * livetime_to_add measured_excess += obs_measured_excess predicted_excess += obs_predicted_excess n_on += n_on_obs n_off += n_off_obs # Fill time interval information if useinterval: int_flux = spectral_model.integral(energy_range[0], energy_range[1]) if n_off > 0.0: alpha_mean /= n_off if livetime > 0.0: alpha_mean_backup /= livetime if alpha_mean == 0.0: # use backup if necessary alpha_mean = alpha_mean_backup flux = measured_excess / predicted_excess.value flux *= int_flux # Gaussian errors, TODO: should be improved flux_err = int_flux / predicted_excess.value delta_excess = excess_error(n_on=n_on, n_off=n_off, alpha=alpha_mean) flux_err *= delta_excess sigma = significance_on_off( n_on=n_on, n_off=n_off, alpha=alpha_mean, method="lima" ) is_ul = sigma <= 3 flux_ul = excess_ul_helene( n_on - alpha_mean * n_off, delta_excess, ul_significance ) flux_ul *= int_flux / predicted_excess.value else: flux = u.Quantity(0, "cm-2 s-1") flux_err = u.Quantity(0, "cm-2 s-1") flux_ul = u.Quantity(-1, "cm-2 s-1") # Store measurements in a dict and return that return ( useinterval, OrderedDict( [ # TODO: check why time is stored without units ("time_min", Time(tmin, format="mjd").value), ("time_max", Time(tmax, format="mjd").value), ("flux", flux), ("flux_err", flux_err), ("flux_ul", flux_ul), ("is_ul", is_ul), ("livetime", livetime), ("alpha", alpha_mean), ("n_on", n_on), ("n_off", n_off), ("measured_excess", measured_excess), ("expected_excess", predicted_excess), ] ), )