# profiles.py: Functions for lightcurve and background time profiles
#
# Authors: William Cleveland (USRA),
# Adam Goldstein (USRA) and
# Daniel Kocevski (NASA)
#
# Portions of the code are Copyright 2020 William Cleveland and
# Adam Goldstein, Universities Space Research Association
# All rights reserved.
#
# Written for the Fermi Gamma-ray Burst Monitor (Fermi-GBM)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
#
from .generators import *
# pulse shapes
[docs]def tophat(x, amp, tstart, tstop):
"""A tophat (rectangular) pulse function.
Args:
x (np.array): Array of times
amp (float): The tophat amplitude
tstart (float): The start time of the tophat
tstop (float): The end time of the tophat
Returns:
np.array: The tophat evaluated at ``x`` times
"""
mask = (x >= tstart) & (x <= tstop)
fxn = np.zeros_like(x)
fxn[mask] = amp
return fxn
[docs]def norris(x, amp, tstart, t_rise, t_decay):
r"""A Norris pulse-shape function:
:math:`I(t) = A \lambda e^{-\tau_1/t - t/\tau_2} \text{ for } t > 0;\\
\text{ where } \lambda = e^{2\sqrt(\tau_1/\tau_2)};`
and where
* :math:`A` is the pulse amplitude
* :math:`\tau_1` is the rise time
* :math:`\tau_2` is the decay time
References:
`Norris, J. P., et al. 2005 ApJ 627 324
<https://iopscience.iop.org/article/10.1086/430294>`_
Args:
x (np.array): Array of times
amp (float): The amplitude of the pulse
tstart (float): The start time of the pulse
t_rise (float): The rise timescal of the pulse
t_decay (flaot): The decay timescale of the pulse
Returns:
np.array: The Norris pulse shape evaluated at ``x`` times
"""
x = np.asarray(x)
fxn = np.zeros_like(x)
mask = (x > tstart)
lam = amp * np.exp(2.0 * np.sqrt(t_rise / t_decay))
fxn[mask] = lam * np.exp(
-t_rise / (x[mask] - tstart) - (x[mask] - tstart) / t_decay)
return fxn
# ------------------------------------------------------------------------------
# background profiles
[docs]def constant(x, amp):
"""A constant background function.
Args:
x (np.array): Array of times
amp (float): The background amplitude
Returns:
np.array: The background evaluated at ``x`` times
"""
fxn = np.empty(x.size)
fxn.fill(amp)
return fxn
[docs]def linear(x, c0, c1):
"""A linear background function.
Args:
x (np.array): Array of times
c0 (float): The constant coefficient
c1 (float): The linear coefficient
Returns:
np.array: The background evaluated at ``x`` times
"""
fxn = c0 + c1 * x
return fxn
[docs]def quadratic(x, c0, c1, c2):
"""A quadratic background function.
Args:
x (np.array): Array of times
c0 (float): The constant coefficient
c1 (float): The linear coefficient
c2 (float): The quadratic coefficient
Returns:
np.array: The background evaluated at ``x`` times
"""
fxn = linear(x, c0, c1) + c2 * x ** 2
return fxn