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https://codeberg.org/Yael-II/MSc2-Project-Chaos.git
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Yael-II
@@ -35,27 +35,35 @@ import numpy as np
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import matplotlib.pyplot as plt
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import time
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import integrator as intg # integrator module
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import kepler_orbit as kep # Analytical & numeric Kepler functions
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import initial_conditions as ic # For initial condition
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import integrator as itg
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import initial_conditions as init
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import potentials as pot
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import energies as ene
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from matplotlib.patches import ConnectionPatch
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if "YII_1" in plt.style.available: plt.style.use("YII_1")
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# ----------------------------
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# 1. Setup & global parameters
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# ----------------------------
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t0 = 0.0
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t0 = 0.0
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T_final = 8.0
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y0 = ic.one_part(1, 0, 0, 1) # [x, y, vx, vy]
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W0 = init.one_part(1, 0, 0, 1) # [x, y, vx, vy]
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h_range = np.logspace(-3.5, -0.1, 25)
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h_range = np.append(h_range, 0.001)
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# For plotting lines/colors
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methods = [
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("Euler", intg.euler, 'o--', 'red'),
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("RK2", intg.rk2, 's--', 'royalblue'),
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("RK4", intg.rk4, '^--', 'limegreen')
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("Euler", itg.euler, 'o--', 'C0'),
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("RK2", itg.rk2, 's--', 'C2'),
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("RK4", itg.rk4, '^--', 'C3')
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]
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colors = {'Analytical': 'navy', 'Euler': 'red', 'RK2': 'royalblue', 'RK4': 'limegreen'}
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colors = {'Analytical': 'k',
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'Euler': 'C0',
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'RK2': 'C2',
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'RK4': 'C3'}
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# Compute machine epsilon
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eps = 1.0
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@@ -70,12 +78,18 @@ time_euler, time_rk2, time_rk4 = [], [], []
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# ------------------------------------------
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# 2. Main loop over step sizes h in h_range
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# ------------------------------------------
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fig, ax = plt.subplots(1)
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for h in h_range:
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ax.cla()
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N = int(T_final / h)
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# Analytical solution
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t_ana, pos_ana, vel_ana, en_ana = kep.kepler_analytical_orb(y0, h, N)
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E_analytical_final = en_ana[-1]
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t_ana, W_ana = itg.kepler_analytical(t0, W0, h, N)
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W_ana_E = np.swapaxes(W_ana, 0, 2)
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W_ana_E = np.swapaxes(W_ana_E, 0, 1)
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E_analytical_final = ene.total(W_ana_E, pot.kepler_potential)
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# Numerical integrators + timing
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all_solutions = {}
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@@ -85,76 +99,167 @@ for h in h_range:
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[time_euler, time_rk2, time_rk4]
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):
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start_time = time.time()
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t_num, y_num = intg.integrator_type(t0, y0, h, N, kep.kepler_orbnum, method)
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t_num, W_num = itg.integrator_type(t0, W0, h, N, pot.kepler_evolution, method)
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elapsed = time.time() - start_time
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store_t.append(elapsed)
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# Final energy error
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en_num = kep.kepler_enrgnum(y_num)
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E_numerical_final = en_num[-1]
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store_err.append(abs(E_analytical_final - E_numerical_final))
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W_num_E = np.swapaxes(W_num, 0, 2)
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W_num_E = np.swapaxes(W_num_E, 0, 1)
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E_numerical_final = ene.total(W_num_E, pot.kepler_potential)
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store_err.append(np.max(abs(E_analytical_final - E_numerical_final)))
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all_solutions[label] = y_num
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all_solutions[label] = W_num
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# Orbit plot (optional, can comment out if too many figures)
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eu_vals = all_solutions["Euler"]
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rk2_vals = all_solutions["RK2"]
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rk4_vals = all_solutions["RK4"]
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fig, ax = plt.subplots(figsize=(6, 6))
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ax.plot(pos_ana[:, 0], pos_ana[:, 1], '-.', color=colors['Analytical'],
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label="Analytical", zorder=4)
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ax.plot(eu_vals[:, 0, 0], eu_vals[:, 0, 1], color=colors['Euler'], label="Euler")
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ax.plot(rk2_vals[:, 0, 0], rk2_vals[:, 0, 1], color=colors['RK2'], label="RK2")
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ax.plot(rk4_vals[:, 0, 0], rk4_vals[:, 0, 1], color=colors['RK4'], label="RK4")
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ax.set_title(f"Orbit for dt = {h:.4g}")
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ax.set_xlabel("x position(reduced units)")
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ax.set_ylabel("y position(reduced units)")
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ax.legend(loc="best")
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ax.grid(True, which='both', ls='--', alpha=0.5)
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plt.tight_layout()
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plt.savefig(f"orbit_dt_{h:.4g}.png", dpi=300, bbox_inches='tight')
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plt.show()
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ax.plot(W_ana[:, 0, 0],
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W_ana[:, 0, 1],
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"-.",
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color=colors['Analytical'],
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label="Analytical",
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zorder=4)
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ax.plot(eu_vals[:, 0, 0],
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eu_vals[:, 0, 1],
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"-",
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color=colors['Euler'],
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label="Euler")
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ax.plot(rk2_vals[:, 0, 0],
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rk2_vals[:, 0, 1],
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"--",
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color=colors['RK2'],
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label="RK2")
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ax.plot(rk4_vals[:, 0, 0],
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rk4_vals[:, 0, 1],
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":",
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color=colors['RK4'],
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label="RK4")
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ax.set_title("$\\Var{{t}} = {:.4f}$".format(h))
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ax.set_xlabel("$x$")
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ax.set_ylabel("$y$")
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ax.set_aspect("equal")
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ax.legend(loc="upper right")
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fig.tight_layout()
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fig.savefig("Figs/orbit_dt_{:.4f}.pdf".format(h))
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if h == h_range[-1]:
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mosaic = ("AB\n"
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"AC")
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fig, axs = plt.subplot_mosaic(mosaic)
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axs = list(axs.values())
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for i in [0,1,2]:
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axs[i].plot(W_ana[:, 0, 0],
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W_ana[:, 0, 1],
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"-.",
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color=colors['Analytical'],
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label="Analytical")
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axs[i].plot(eu_vals[:, 0, 0],
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eu_vals[:, 0, 1],
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"-",
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color=colors['Euler'],
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label="Euler")
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axs[i].plot(rk2_vals[:, 0, 0],
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rk2_vals[:, 0, 1],
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"--",
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color=colors['RK2'],
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label="RK2")
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axs[i].plot(rk4_vals[:, 0, 0],
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rk4_vals[:, 0, 1],
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":",
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color=colors['RK4'],
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label="RK4")
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axs[i].set_aspect("equal")
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fig.suptitle("$\\Var{{t}} = {:.4f}$".format(h))
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axs[0].set_xlabel("$x$")
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axs[0].set_ylabel("$y$")
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axs[0].legend(loc="upper left")
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win_1 = 0.02
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axs[1].set_xlim(0 - win_1, 0 + win_1)
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axs[1].set_ylim(1 - win_1, 1 + win_1)
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#axs[0].indicate_inset_zoom(axs[1], lw=1)
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win_2 = 1e-6
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axs[2].set_xlim(0 - win_2, 0 + win_2)
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axs[2].set_ylim(1 - win_2, 1 + win_2)
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#axs[1].indicate_inset_zoom(axs[2], lw=1)
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ln1 = ConnectionPatch(xyA=(0,1), xyB=(0-win_1,1+win_1),
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coordsA="data", coordsB="data",
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axesA=axs[0], axesB=axs[1],
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color="k", lw=1, alpha=0.5)
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ln2 = ConnectionPatch(xyA=(0,1), xyB=(0-win_1,1-win_1),
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coordsA="data", coordsB="data",
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axesA=axs[0], axesB=axs[1],
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color="k", lw=1, alpha=0.5)
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fig.add_artist(ln1)
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fig.add_artist(ln2)
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ln3 = ConnectionPatch(xyA=(0,1), xyB=(0-win_2,1+win_2),
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coordsA="data", coordsB="data",
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axesA=axs[1], axesB=axs[2],
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color="k", lw=1, alpha=0.5)
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ln4 = ConnectionPatch(xyA=(0,1), xyB=(0+win_2,1+win_2),
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coordsA="data", coordsB="data",
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axesA=axs[1], axesB=axs[2],
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color="k", lw=1, alpha=0.5)
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fig.add_artist(ln3)
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fig.add_artist(ln4)
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#fig.tight_layout()
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fig.savefig("Figs/orbit_dt.pdf")
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# ---------------------------------------------------------------
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# 3. Summary Plots: CPU time and final energy error (Log-Log)
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# ---------------------------------------------------------------
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# --- Step size vs. CPU Time (Log-Log) ---
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fig, ax = plt.subplots(figsize=(8, 6))
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ax.loglog(h_range, time_euler, 'o--', color='red', label="Euler")
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ax.loglog(h_range, time_rk2, 's--', color='royalblue', label="RK2")
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ax.loglog(h_range, time_rk4, '^--', color='limegreen', label="RK4")
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fig, ax = plt.subplots()
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ax.plot(h_range[:-1], time_euler[:-1], 'o-', color='C0', label="Euler")
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ax.plot(h_range[:-1], time_rk2[:-1], 's--', color='C2', label="RK2")
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ax.plot(h_range[:-1], time_rk4[:-1], '^:', color='C3', label="RK4")
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ax.set_xlabel(r"Step size $(\Delta t)$", fontsize=12)
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ax.set_ylabel("CPU Time (s)", fontsize=12)
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ax.set_title(r"$\Delta t$ vs. CPU Time ", fontsize=14)
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ax.minorticks_on()
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ax.grid(True, which="major", linestyle="--", linewidth=0.5, alpha=0.7)
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ax.grid(True, which="minor", linestyle=":", linewidth=0.5, alpha=0.5)
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ax.legend(loc="best", fontsize=12)
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plt.tight_layout()
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plt.savefig("dt_vs_cpu_time_loglog.png", dpi=300, bbox_inches='tight')
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plt.show()
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ax.set_xscale("log")
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ax.set_yscale("log")
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ax.set_xlabel("Step size $\\Var{{t}}$")
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ax.set_ylabel("CPU Time $t_\\mathrm{CPU}\\axunit{{s}}$")
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#ax.minorticks_on()
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#ax.grid(True, which="major", linestyle="--", linewidth=0.5, alpha=0.7)
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#ax.grid(True, which="minor", linestyle=":", linewidth=0.5, alpha=0.5)
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ax.legend(loc="best")
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fig.tight_layout()
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fig.savefig("Figs/dt_vs_cpu_time_loglog.pdf")
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# --- Step size vs. Final Energy Error (Log-Log) ---
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fig, ax = plt.subplots(figsize=(8, 6))
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ax.loglog(h_range, err_euler, 'o--', color='red', label="Euler")
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ax.loglog(h_range, err_rk2, 's--', color='royalblue', label="RK2")
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ax.loglog(h_range, err_rk4, '^--', color='limegreen', label="RK4")
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fig, ax = plt.subplots()
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ax.plot(h_range[:-1], err_euler[:-1], 'o-', color='C0', label="Euler")
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ax.plot(h_range[:-1], err_rk2[:-1], 's--', color='C2', label="RK2")
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ax.plot(h_range[:-1], err_rk4[:-1], '^:', color='C3', label="RK4")
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ax.set_xscale("log")
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ax.set_yscale("log")
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# Machine Epsilon line (horizontal)
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ax.axhline(eps, color='darkred', ls='--', label='Machine Epsilon')
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ax.axhline(eps, color='darkred', ls='-.',
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label='Machine precision $\\epsilon$')
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ax.set_xlabel(r"Step size $(\Delta t)$", fontsize=12)
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ax.set_ylabel(r"$|E_{\mathrm{analytical}} - E_{\mathrm{numerical}}|$", fontsize=12)
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ax.set_title(r"$\Delta t$ vs. Final Energy Error ", fontsize=14)
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ax.minorticks_on()
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ax.grid(True, which="major", linestyle="--", linewidth=0.5, alpha=0.7)
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ax.grid(True, which="minor", linestyle=":", linewidth=0.5, alpha=0.5)
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ax.set_xlabel("Step size $\\Var{{t}}$")
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ax.set_ylabel("$\\abs{{E_{\\mathrm{analytical}} - E_{\\mathrm{numerical}}}}$")
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#ax.minorticks_on()
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#ax.grid(True, which="major", linestyle="--", linewidth=0.5, alpha=0.7)
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#ax.grid(True, which="minor", linestyle=":", linewidth=0.5, alpha=0.5)
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# Ensure 'Machine Epsilon' is in legend
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"""
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handles, labels = ax.get_legend_handles_labels()
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if 'Machine Epsilon' not in labels:
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import matplotlib.lines as mlines
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@@ -162,8 +267,9 @@ if 'Machine Epsilon' not in labels:
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handles.append(h_me)
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labels.append('Machine Epsilon')
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ax.legend(handles, labels, loc="best", fontsize=12)
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plt.tight_layout()
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plt.savefig("timestep_vs_final_energy_error_loglog1.png", dpi=300, bbox_inches='tight')
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"""
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ax.legend()
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fig.tight_layout()
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fig.savefig("Figs/timestep_vs_final_energy_error_loglog1.pdf")
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plt.show()
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