added Gottwald Melbourne methode

Source/gottwald_melbourne.py

@@ -0,0 +1,137 @@
+#!/usr/bin/env python
+"""
+Gottwald and Melbourne method
+
+Study chaotic behaviour with the method of Gottwald & Melbourne (2003).
+
+@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
+@ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
+                de Strasbourg, UMR 7550, F-67000 Strasbourg, France
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+gottwald_melbourne.py
+Copyright (C) 2025 Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+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/.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.integrate import cumulative_trapezoid
+
+import potentials as pot
+import integrator as itg
+import initial_conditions as init
+
+# -----------------------------------------------------------------------------------
+# Parameters
+# -----------------------------------------------------------------------------------
+DEFAULT_N_iter = 30000
+DEFAULT_h = 0.01
+DEFAULT_c = 1.7
+
+E_all = np.array([1/100, 1/12, 1/10, 1/8, 1/6])
+
+if "YII_1" in plt.style.available: plt.style.use("YII_1")
+
+# -----------------------------------------------------------------------------------
+# 1) Integrate Hénon–Heiles and Return x(t), etc.
+# -----------------------------------------------------------------------------------
+def compute_coordinates(E: float,
+                        N_iter: int = DEFAULT_N_iter,
+                        h: float = DEFAULT_h,
+                        N_part: int = 1) -> tuple:
+    """
+    Integrate Hénon–Heiles for N_iter steps at step size h for a single
+    random initial condition at energy E.
+    Returns:
+      t_part: array of times of length N_iter
+      x_part, y_part, u_part, v_part: arrays of length N_iter each
+    """
+    # Generate 1 initial condition at energy E
+    W_init = init.n_energy_part(pot.hh_potential, N_part, E)
+    W0 = W_init[:, :, 0]  # take first particle
+
+    # Perform integration using RK4
+    final_t, sol_array = itg.rk4(0.0, W0, h, N_iter, pot.hh_evolution)
+    # Reconstruct the time array using step size and number of iterations
+
+    # Extract coordinate arrays
+    x_part = sol_array[:, 0, 0]
+    y_part = sol_array[:, 0, 1]
+    u_part = sol_array[:, 1, 0]
+    v_part = sol_array[:, 1, 1]
+
+    return final_t, x_part, y_part, u_part, v_part
+
+# -----------------------------------------------------------------------------------
+# 2) Compute theta(t_i) in discrete form
+# -----------------------------------------------------------------------------------
+def compute_theta_discrete(t_array, x_array, c=DEFAULT_c):
+    int_x = cumulative_trapezoid(x_array, t_array, initial=0.0)
+    theta_array = c * t_array + int_x
+    return theta_array
+
+# -----------------------------------------------------------------------------------
+# 3) Compute p(t_i) in discrete form
+# -----------------------------------------------------------------------------------
+def compute_p_discrete(t_array, x_array, theta_array):
+    integrand = x_array * np.cos(theta_array)
+    p_array = cumulative_trapezoid(integrand, t_array, initial=0.0)
+    return p_array
+
+# -----------------------------------------------------------------------------------
+# Main: Compute p(t) for each energy and plot on a single graph
+# -----------------------------------------------------------------------------------
+if __name__ == "__main__":
+    fig, ax = plt.subplots()  # single figure and axis
+
+    # Loop over energies and plot each p(t) on the same axis
+    i = 0
+    line_styles = ["-", "-", "--", ":", ":"]
+    for E in E_all:
+        # 1) Integrate Hénon–Heiles for current energy
+        t_part, x_part, y_part, u_part, v_part = compute_coordinates(E)
+
+        # 2) Compute theta(t) for current energy
+        theta_arr = compute_theta_discrete(t_part, x_part, c=DEFAULT_c)
+
+        # 3) Compute p(t) for current energy
+        p_arr = compute_p_discrete(t_part, x_part, theta_arr)
+
+        # Plot p(t) for the current energy on the same axis
+        ax.plot(t_part, p_arr, 
+                line_styles[i], 
+                color="C{}".format(i).replace("C1", "C5"),
+                label="$E={:.3f}$".format(E))
+        i += 1
+
+    #ax.set_title("$p(t)$ (Melbourne–Gottwald Test)")
+    ax.set_xlabel("$t$")
+    ax.set_ylabel("$p(t)$")
+    ax.legend()
+
+    # Enable both major and minor gridlines
+    #ax.grid(which='both', linestyle='--', linewidth=0.5)
+    #ax.minorticks_on()
+
+    fig.tight_layout()
+    fig.savefig("Figs/gottwald_melbourne.pdf")
+    plt.show()
+