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r"""
.. _gaussian-temporal-model:
Gaussian temporal model
=======================
This model parametrises a gaussian time model.
.. math::
F(t) = \exp \left( -0.5 \cdot \frac{ (t - t_{\rm{ref}})^2 } { \sigma^2 } \right)
"""
# %%
# Example plot
# ------------
# Here is an example plot of the model:
from astropy import units as u
from astropy.time import Time
import matplotlib.pyplot as plt
from gammapy.modeling.models import (
GaussianTemporalModel,
Models,
PowerLawSpectralModel,
SkyModel,
)
sigma = "3 h"
t_ref = Time("2020-10-01")
time_range = [t_ref - 0.5 * u.d, t_ref + 0.5 * u.d]
gaussian_model = GaussianTemporalModel(t_ref=t_ref.mjd * u.d, sigma=sigma)
gaussian_model.plot(time_range)
plt.grid(which="both")
# %%
# YAML representation
# -------------------
# Here is an example YAML file using the model:
model = SkyModel(
spectral_model=PowerLawSpectralModel(),
temporal_model=gaussian_model,
name="gaussian_model",
)
models = Models([model])
print(models.to_yaml())
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