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124 lines
3.8 KiB
Python
124 lines
3.8 KiB
Python
#!/usr/bin/env python
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"""
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Integrator
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Integrate differential equations.
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@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
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@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
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de Strasbourg, UMR 7550, F-67000 Strasbourg, France
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@ Date: 2025-01-01
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Licence:
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Order and Chaos in a 2D potential
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Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
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Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
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integrator.py
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Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
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Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
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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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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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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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import numpy as np
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def euler(x0, y0, h, n, func): # FIXME cannot be used with vectors
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"""DEPRECIATED - DO NOT USE
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Euler method adapted for state vector [[x, y], [u, v]]
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:param x0: initial time value
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:param y0: initial state vector [[x, y], [u, v]]
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:param h: step size (time step)
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:param n: number of steps
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:param func: RHS of differential equation
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:returns: x array, solution array
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"""
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x_values = np.zeros(n)
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y_values = np.zeros((n, 2, 2)) # to accommodate the state vector
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for i in range(n):
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dydt = func(x0, y0)
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y0 = y0 + h * dydt
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x0 = x0 + h
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x_values[i] = x0
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y_values[i, :, :] = y0
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return x_values, y_values
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# Updated RK2 integrator
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def rk2(x0, y0, h, n, func): # FIXME cannot be used with vectors
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""" DEPRECIATED - DO NOT USE
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RK2 method adapted for state vector [[x, y], [u, v]]
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:param x0: initial time value
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:param y0: initial state vector [[x, y], [u, v]]
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:param h: step size (time step)
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:param n: number of steps
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:param func: RHS of differential equation
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:returns: x array, solution array
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"""
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x_values = np.zeros(n)
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y_values = np.zeros((n, 2, 2)) # to accommodate the state vector
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for i in range(n):
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k1 = func(x0, y0)
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k2 = func(x0 + h / 2., y0 + h / 2. * k1)
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y0 = y0 + h * (k1 / 2. + k2 / 2.)
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x0 = x0 + h
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x_values[i] = x0
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y_values[i, :, :] = y0
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return x_values, y_values
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def rk4(t0: float,
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W0: np.ndarray,
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h: float,
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n: int,
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func):
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"""RK4 method adapted for state vector [[x, y], [u, v]]
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@ params
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- x0: initial time value
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- y0: initial state vector [[x, y], [u, v]]
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- h: step size (time step)
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- n: number of steps
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- func: RHS of differential equation
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@returns:
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- t, W: time and state (solution) arrays,
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"""
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time = np.zeros(n)
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W = np.zeros((n,) + np.shape(W0))
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# to accommodate the state vector
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t = t0
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w = W0
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for i in range(n):
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k1 = func(t, w)
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k2 = func(t + h / 2., w + h / 2. * k1)
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k3 = func(t + h / 2., w + h / 2. * k2)
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k4 = func(t + h, w + h * k3)
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w = w + h * (k1 / 6. + k2 / 3. + k3 / 3. + k4 / 6.)
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t = t + h
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time[i] = t
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W[i] = w
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return t, W
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def integrator_type(x0, y0, h, n, func, int_type):
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"""DEPRECIATED - DO NOT USE"""
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return int_type(x0, y0, h, n, func)
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