Source code for gammapy.time.models

# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
import numpy as np
from astropy.utils import lazyproperty
from astropy import units as u
from astropy.table import Table
from ..utils.scripts import make_path
from ..utils.time import time_ref_from_dict
from ..utils.fitting import Parameter, Parameters

__all__ = ["PhaseCurveTableModel", "LightCurveTableModel"]


[docs]class PhaseCurveTableModel(object): """Temporal phase curve model. Phase for a given time is computed as .. math:: \phi(t) = \phi_0 + f_0(t-t_0) + (1/2)f_1(t-t_0)^2 + (1/6)f_2(t-t_0)^3 Strictly periodic sources such as gamma-ray binaries have ``f1=0`` and ``f2=0``. Sources like some pulsars where the period spins up or down have ``f1!=0`` and / or ``f2 !=0``. For a binary, ``f0`` should be calculated as 1/T, where T is the period of the binary in unit of ``seconds``. The "phase curve", i.e. multiplicative flux factor for a given phase is given by a `~astropy.table.Table` of nodes ``(phase, norm)``, using linear interpolation and circular behaviour, where ``norm(phase=0) == norm(phase=1)``. Parameters ---------- table : `~astropy.table.Table` A table of 'PHASE' vs 'NORM' should be given time_0 : float The MJD value where phase is considered as 0. phase_0 : float Phase at the reference MJD f0, f1, f2 : float Derivatives of the function phi with time of order 1, 2, 3 in units of ``s^-1, s^-2 & s^-3``, respectively. Examples -------- Create an example phase curve object:: from astropy.table import Table from gammapy.utils.scripts import make_path from gammapy.time.models import PhaseCurveTableModel filename = make_path('$GAMMAPY_EXTRA/test_datasets/phasecurve_LSI_DC.fits') table = Table.read(str(filename)) phase_curve = PhaseCurveTableModel(table, time_0=43366.275, phase_0=0.0, f0=4.367575e-7, f1=0.0, f2=0.0) Use it to compute a phase and evaluate the phase curve model for a given time: >>> phase_curve.phase(time=46300.0) 0.7066006737999402 >>> phase_curve.evaluate_norm_at_time(46300) 0.49059393580053845 """ def __init__(self, table, time_0, phase_0, f0, f1, f2): self.table = table self.parameters = Parameters( [ Parameter("time_0", time_0), Parameter("phase_0", phase_0), Parameter("f0", f0), Parameter("f1", f1), Parameter("f2", f2), ] )
[docs] def phase(self, time): """Evaluate phase for a given time. Parameters ---------- time : array_like Returns ------- phase : array_like """ pars = self.parameters time_0 = pars["time_0"].value phase_0 = pars["phase_0"].value f0 = pars["f0"].value f1 = pars["f1"].value f2 = pars["f2"].value t = (time - time_0) * u.day.to(u.second) phase = self._evaluate_phase(t, phase_0, f0, f1, f2) return np.remainder(phase, 1)
@staticmethod def _evaluate_phase(t, phase_0, f0, f1, f2): return phase_0 + t * (f0 + t * (f1 / 2 + f2 / 6 * t))
[docs] def evaluate_norm_at_time(self, time): """Evaluate for a given time. Parameters ---------- time : array_like Time since the ``reference`` time. Returns ------- norm : array_like """ phase = self.phase(time) return self.evaluate_norm_at_phase(phase)
[docs] def evaluate_norm_at_phase(self, phase): xp = self.table["PHASE"] fp = self.table["NORM"] return np.interp(x=phase, xp=xp, fp=fp, period=1)
[docs]class LightCurveTableModel(object): """Temporal light curve model. The lightcurve is given as a table with columns ``time`` and ``norm``. The ``norm`` is supposed to be a unite-less multiplicative factor in the model, to be multiplied with a spectral model. The model does linear interpolation for times between the given ``(time, norm)`` values. The implementation currently uses `scipy.interpolate.InterpolatedUnivariateSpline`, using degree ``k=1`` to get linear interpolation. This class also contains an ``integral`` method, making the computation of mean fluxes for a given time interval a one-liner. Parameters ---------- table : `~astropy.table.Table` A table with 'TIME' vs 'NORM' Examples -------- Read an example light curve object: >>> from gammapy.time.models import LightCurveTableModel >>> path = '$GAMMAPY_EXTRA/test_datasets/models/light_curve/lightcrv_PKSB1222+216.fits' >>> light_curve = LightCurveTableModel.read(path) Show basic information about the lightcurve: >>> print(light_curve) LightCurve model summary: Start time: 59000.5 MJD End time: 61862.5 MJD Norm min: 0.01551196351647377 Norm max: 1.0 Compute ``norm`` at a given time: >>> light_curve.evaluate_norm_at_time(46300) 0.49059393580053845 Compute mean ``norm`` in a given time interval: >>> light_curve.mean_norm_in_time_interval(46300, 46301) """ def __init__(self, table): self.table = table def __str__(self): ss = "LightCurveTableModel model summary:\n" ss += "Start time: {} MJD\n".format(self._time[0].mjd) ss += "End time: {} MJD\n".format(self._time[-1].mjd) ss += "Norm min: {}\n".format(self.table["NORM"].min()) ss += "Norm max: {}\n".format(self.table["NORM"].max()) return ss
[docs] @classmethod def read(cls, path): """Read lightcurve model table from FITS file. TODO: This doesn't read the XML part of the model yet. """ path = make_path(path) table = Table.read(str(path)) return cls(table)
@lazyproperty def _interpolator(self): from scipy.interpolate import InterpolatedUnivariateSpline x = self.table["TIME"].data y = self.table["NORM"].data return InterpolatedUnivariateSpline(x, y, k=1) @lazyproperty def _time_ref(self): return time_ref_from_dict(self.table.meta) @lazyproperty def _time(self): return self._time_ref + self.table["TIME"].data * u.s
[docs] def evaluate_norm_at_time(self, time): """Evaluate for a given time. Parameters ---------- time : array_like Time since the ``reference`` time. Returns ------- norm : array_like """ return self._interpolator(time)
[docs] def mean_norm_in_time_interval(self, time_min, time_max): """Compute mean ``norm`` in a given time interval. TODO: vectorise, i.e. allow arrays of time intervals in a single call. Parameters ---------- time_min, time_max : float Time interval Returns ------- norm : float Mean norm """ dt = time_max - time_min integral = self._interpolator.integral(time_min, time_max) return integral / dt