PhaseCurveTemplateTemporalModel¶

class gammapy.modeling.models.PhaseCurveTemplateTemporalModel(table, time_0, phase_0, f0, f1=0, f2=0)[source]¶

Bases: gammapy.modeling.models.TemporalModel

Temporal phase curve model.

Phase for a given time is computed as:

\[\phi(t) = \phi_0 + f_0(t-t_0) + (1/2)f_1(t-t_0)^2 + (1/6)f_2(t-t_0)^3\]

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 Table of nodes (phase, norm), using linear interpolation and circular behaviour, where norm(phase=0) == norm(phase=1).

Parameters

tableTable: A table of ‘PHASE’ vs ‘NORM’ should be given
time_0float: The MJD value where phase is considered as 0.
phase_0float: Phase at the reference MJD
f0, f1, f2float: 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.modeling.models import PhaseCurveTemplateTemporalModel
filename = make_path('$GAMMAPY_DATA/tests/phasecurve_LSI_DC.fits')
table = Table.read(filename)
phase_curve = PhaseCurveTemplateTemporalModel(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

Attributes Summary

`default_parameters`
`f0`	A model parameter.
`f1`	A model parameter.
`f2`	A model parameter.
`parameters`	Parameters (`Parameters`)
`phase_0`	A model parameter.
`tag`
`time_0`	A model parameter.

Methods Summary

`copy`(self)	A deep copy.
`create`(tag, \args, \\*kwargs)	Create a model instance.
`evaluate_norm_at_phase`(self, phase)
`evaluate_norm_at_time`(self, time)	Evaluate for a given time.
`from_dict`(data)
`phase`(self, time)	Evaluate phase for a given time.
`sample_time`(self, n_events, t_min, t_max[, …])	Sample arrival times of events.
`to_dict`(self)	Create dict for YAML serialisation

Attributes Documentation

default_parameters = <gammapy.modeling.parameter.Parameters object>¶

f0¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

f1¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

f2¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

parameters¶: Parameters (Parameters)

phase_0¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

tag = 'PhaseCurveTemplateTemporalModel'¶

time_0¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

Methods Documentation

copy(self)¶: A deep copy.

static create(tag, *args, **kwargs)¶

Create a model instance.

Examples

>>> from gammapy.modeling import Model
>>> spectral_model = Model.create("PowerLaw2SpectralModel", amplitude="1e-10 cm-2 s-1", index=3)
>>> type(spectral_model)
gammapy.modeling.models.spectral.PowerLaw2SpectralModel

evaluate_norm_at_phase(self, phase)[source]¶

evaluate_norm_at_time(self, time)[source]¶

Evaluate for a given time.

Parameters

timearray_like: Time since the reference time.

Returns

normarray_like

classmethod from_dict(data)¶

phase(self, time)[source]¶

Evaluate phase for a given time.

Parameters

timearray_like

Returns

phasearray_like

sample_time(self, n_events, t_min, t_max, t_delta='1 s', random_state=0)[source]¶

Sample arrival times of events.

Parameters

n_eventsint: Number of events to sample.
t_minTime: Start time of the sampling.
t_maxTime: Stop time of the sampling.
t_deltaQuantity: Time step used for sampling of the temporal model.
random_state{int, ‘random-seed’, ‘global-rng’, RandomState}: Defines random number generator initialisation. Passed to get_random_state.

Returns

timeQuantity: Array with times of the sampled events.

to_dict(self)¶: Create dict for YAML serialisation