mirror of
https://codeberg.org/Yael-II/MSc2-Project-Chaos.git
synced 2026-03-15 04:16:26 +01:00
new test
This commit is contained in:
Yael-II
169
Source/test_integrators.py
Normal file
169
Source/test_integrators.py
Normal file
@@ -0,0 +1,169 @@
|
||||
"""
|
||||
Test: Integrators
|
||||
|
||||
Demonstrating Keplerian 2-body orbits using various integrators,
|
||||
and comparing accuracy and runtime over a range of step sizes.
|
||||
|
||||
@ 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)
|
||||
|
||||
test_integrators.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
|
||||
import time
|
||||
|
||||
import integrator as intg # integrator module
|
||||
import kepler_orbit as kep # Analytical & numeric Kepler functions
|
||||
import initial_conditions as ic # For initial condition
|
||||
|
||||
# ----------------------------
|
||||
# 1. Setup & global parameters
|
||||
# ----------------------------
|
||||
t0 = 0.0
|
||||
T_final = 8.0
|
||||
y0 = ic.one_part(1, 0, 0, 1) # [x, y, vx, vy]
|
||||
|
||||
|
||||
h_range = np.logspace(-3.5, -0.1, 25)
|
||||
|
||||
# For plotting lines/colors
|
||||
methods = [
|
||||
("Euler", intg.euler, 'o--', 'red'),
|
||||
("RK2", intg.rk2, 's--', 'royalblue'),
|
||||
("RK4", intg.rk4, '^--', 'limegreen')
|
||||
]
|
||||
colors = {'Analytical': 'navy', 'Euler': 'red', 'RK2': 'royalblue', 'RK4': 'limegreen'}
|
||||
|
||||
# Compute machine epsilon
|
||||
eps = 1.0
|
||||
while 1.0 + eps/2 > 1.0:
|
||||
eps /= 2.0
|
||||
print(f"Machine epsilon: {eps}")
|
||||
|
||||
# Arrays to store final energy errors & times
|
||||
err_euler, err_rk2, err_rk4 = [], [], []
|
||||
time_euler, time_rk2, time_rk4 = [], [], []
|
||||
|
||||
# ------------------------------------------
|
||||
# 2. Main loop over step sizes h in h_range
|
||||
# ------------------------------------------
|
||||
for h in h_range:
|
||||
N = int(T_final / h)
|
||||
|
||||
# Analytical solution
|
||||
t_ana, pos_ana, vel_ana, en_ana = kep.kepler_analytical_orb(y0, h, N)
|
||||
E_analytical_final = en_ana[-1]
|
||||
|
||||
# Numerical integrators + timing
|
||||
all_solutions = {}
|
||||
for (label, method, *_), store_err, store_t in zip(
|
||||
methods,
|
||||
[err_euler, err_rk2, err_rk4],
|
||||
[time_euler, time_rk2, time_rk4]
|
||||
):
|
||||
start_time = time.time()
|
||||
t_num, y_num = intg.integrator_type(t0, y0, h, N, kep.kepler_orbnum, method)
|
||||
elapsed = time.time() - start_time
|
||||
|
||||
store_t.append(elapsed)
|
||||
|
||||
# Final energy error
|
||||
en_num = kep.kepler_enrgnum(y_num)
|
||||
E_numerical_final = en_num[-1]
|
||||
store_err.append(abs(E_analytical_final - E_numerical_final))
|
||||
|
||||
all_solutions[label] = y_num
|
||||
|
||||
# Orbit plot (optional, can comment out if too many figures)
|
||||
eu_vals = all_solutions["Euler"]
|
||||
rk2_vals = all_solutions["RK2"]
|
||||
rk4_vals = all_solutions["RK4"]
|
||||
|
||||
fig, ax = plt.subplots(figsize=(6, 6))
|
||||
ax.plot(pos_ana[:, 0], pos_ana[:, 1], '-.', color=colors['Analytical'],
|
||||
label="Analytical", zorder=4)
|
||||
ax.plot(eu_vals[:, 0, 0], eu_vals[:, 0, 1], color=colors['Euler'], label="Euler")
|
||||
ax.plot(rk2_vals[:, 0, 0], rk2_vals[:, 0, 1], color=colors['RK2'], label="RK2")
|
||||
ax.plot(rk4_vals[:, 0, 0], rk4_vals[:, 0, 1], color=colors['RK4'], label="RK4")
|
||||
ax.set_title(f"Orbit for dt = {h:.4g}")
|
||||
ax.set_xlabel("x position(reduced units)")
|
||||
ax.set_ylabel("y position(reduced units)")
|
||||
ax.legend(loc="best")
|
||||
ax.grid(True, which='both', ls='--', alpha=0.5)
|
||||
plt.tight_layout()
|
||||
plt.savefig(f"orbit_dt_{h:.4g}.png", dpi=300, bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
# ---------------------------------------------------------------
|
||||
# 3. Summary Plots: CPU time and final energy error (Log-Log)
|
||||
# ---------------------------------------------------------------
|
||||
|
||||
# --- Step size vs. CPU Time (Log-Log) ---
|
||||
fig, ax = plt.subplots(figsize=(8, 6))
|
||||
ax.loglog(h_range, time_euler, 'o--', color='red', label="Euler")
|
||||
ax.loglog(h_range, time_rk2, 's--', color='royalblue', label="RK2")
|
||||
ax.loglog(h_range, time_rk4, '^--', color='limegreen', label="RK4")
|
||||
|
||||
ax.set_xlabel(r"Step size $(\Delta t)$", fontsize=12)
|
||||
ax.set_ylabel("CPU Time (s)", fontsize=12)
|
||||
ax.set_title(r"$\Delta t$ vs. CPU Time ", fontsize=14)
|
||||
ax.minorticks_on()
|
||||
ax.grid(True, which="major", linestyle="--", linewidth=0.5, alpha=0.7)
|
||||
ax.grid(True, which="minor", linestyle=":", linewidth=0.5, alpha=0.5)
|
||||
ax.legend(loc="best", fontsize=12)
|
||||
plt.tight_layout()
|
||||
plt.savefig("dt_vs_cpu_time_loglog.png", dpi=300, bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
# --- Step size vs. Final Energy Error (Log-Log) ---
|
||||
fig, ax = plt.subplots(figsize=(8, 6))
|
||||
ax.loglog(h_range, err_euler, 'o--', color='red', label="Euler")
|
||||
ax.loglog(h_range, err_rk2, 's--', color='royalblue', label="RK2")
|
||||
ax.loglog(h_range, err_rk4, '^--', color='limegreen', label="RK4")
|
||||
|
||||
# Machine Epsilon line (horizontal)
|
||||
ax.axhline(eps, color='darkred', ls='--', label='Machine Epsilon')
|
||||
|
||||
ax.set_xlabel(r"Step size $(\Delta t)$", fontsize=12)
|
||||
ax.set_ylabel(r"$|E_{\mathrm{analytical}} - E_{\mathrm{numerical}}|$", fontsize=12)
|
||||
ax.set_title(r"$\Delta t$ vs. Final Energy Error ", fontsize=14)
|
||||
ax.minorticks_on()
|
||||
ax.grid(True, which="major", linestyle="--", linewidth=0.5, alpha=0.7)
|
||||
ax.grid(True, which="minor", linestyle=":", linewidth=0.5, alpha=0.5)
|
||||
|
||||
# Ensure 'Machine Epsilon' is in legend
|
||||
handles, labels = ax.get_legend_handles_labels()
|
||||
if 'Machine Epsilon' not in labels:
|
||||
import matplotlib.lines as mlines
|
||||
h_me = mlines.Line2D([], [], color='darkred', ls='--', label='Machine Epsilon')
|
||||
handles.append(h_me)
|
||||
labels.append('Machine Epsilon')
|
||||
ax.legend(handles, labels, loc="best", fontsize=12)
|
||||
|
||||
plt.tight_layout()
|
||||
plt.savefig("timestep_vs_final_energy_error_loglog1.png", dpi=300, bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
Reference in New Issue
Block a user