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