def testFig8Lce(self): # takes a long time, so its disabled
sys = NBodySystem(body_masses=[1, 1, 1], G=1)
solver = SystemSolver(sys)
tspan = [0, 1.5]
y0 = np.zeros(2 * sys.body_dim * len(sys.body_masses),
dtype=np.float64)
x1 = np.array([0.97000436, -0.24308753, 0])
x3p = np.array([-0.93240737, -0.86473146, 0])
y0[0:3] = x1
y0[3:6] = -x1
y0[6:9] = 0
y0[9:12] = -x3p / 2
y0[12:15] = -x3p / 2
y0[15:18] = x3p
# print(sys.fun(np.zeros_like(y0), y0).reshape(6, -1))
lce, run = solver.get_lce(tspan[1], y0)
t = run['results'].t[1:]
y = run['results'].y[sys.dim:, 1:].reshape(sys.dim, sys.dim, -1)
#print(y[:, :, -1])
lces = []
for i, t_val in enumerate(t):
Df_y = y[:, :, i]
lces.append(solver.calc_lce(Df_y, t_val))
print(lces[-1])
print(np.mean(lces[-5:]))
clearFigs()
plt.figure()
plt.plot(t, lces)
plt.show(True)
def testExample(self):
sys = RestrictedCircular3Body()
slv = SystemSolver(sys)
lce, lce_run = slv.get_lce()
slv.calc_lce
# print(lce)
init = [1, -1, 1, -1]
run = slv.run([0, 5], init)
run['results'].y = run['results'].y[:2, :]
slv.plot2d(run)
def testLCEPendulumLong(self):
sys = DoublePendulumSystem()
slv = SystemSolver(sys)
theta = pi * 120 / 180
lce, run = slv.get_lce(T=100, y0=[theta, 0, 0, 0])
y = run['results'].y
Df_y0 = y[sys.dim:, -1].reshape(sys.dim, sys.dim)
print(Df_y0)
print(lce)
self.assertGreater(lce, 0)
def testLCEPendulumVaryAngle(self):
sys = DoublePendulumSystem()
slv = SystemSolver(sys)
thetas = []
lces = []
for theta in np.arange(0.001, pi + 0.0001, pi / 20):
lce, _ = slv.get_lce(T=100, y0=[theta, 0, 0, 0])
thetas.append(theta)
lces.append(lce)
clearFigs()
plt.figure()
plt.plot(thetas, lces)
plt.show(True)
def testLCE(self):
# slv.calc_lce(Df_y0, T)
sys = RestrictedCircular3Body()
slv = SystemSolver(sys)
lce, lce_run = slv.get_lce(T=100)
t = lce_run['results'].t
y = lce_run['results'].y
sys_dim = sys.dim
lces = []
start_t = 10
for i in range(start_t, t.shape[0]):
Df_y0 = y[sys_dim:, i].reshape(sys_dim, sys_dim)
lce = slv.calc_lce(Df_y0, t[i])
lces.append(lce)
plt.plot(t[start_t:], lces)
plt.show(True)
def runLCETest(self, sigma, rho, beta, l1):
sys = LorenzSystem(sigma, rho, beta)
slv = SystemSolver(sys)
lce, run = slv.get_lce(T=100)
T0 = 0
t = run['results'].t[T0:]
y = run['results'].y[:, T0:]
lces = []
for i, t_val in enumerate(t):
Df_y0 = y[sys.dim:, i].reshape(sys.dim, sys.dim)
lces.append(slv.calc_lce(Df_y0, t_val))
clearFigs()
plt.figure()
plt.plot(t, lces)
plt.show(True)
print(Df_y0)
print(lce, l1, (lce - l1) / l1)
self.assertAlmostEqual((lce - l1) / l1, 0, places=0)
from echonn.sys import CircleSystem, SystemSolver
if __name__ == "__main__":
sys = SystemSolver(CircleSystem())
lce, run = sys.get_lce()
print('lce:', lce)
print(run['results'].y[2:, -1].reshape(2, 2))
if __name__ == "__main__":
data = [
[16, 45.92, 4, 1.50255],
[16, 40, 4, 1.37446],
[10, 28, 8 / 3, 0.90566],
]
results = []
for sigma, rho, beta, lambda_ in data:
lces = []
print('calculating lces...')
for i in range(10):
sys = LorenzSystem(sigma, rho, beta)
slv = SystemSolver(sys)
lce, _ = slv.get_lce()
print('\t{}:'.format(i), lce)
lces.append(lce)
res = {}
res['beta'] = beta
res['rho'] = rho
res['sigma'] = sigma
res['lambda'] = lambda_
res['mean'] = np.mean(lces)
res['std'] = np.std(lces)
res['error'] = res['mean'] - lambda_
res['relative error'] = res['error'] / lambda_
print(res)
print()
results.append(res)
solver = SystemSolver(sys)
tspan = [0, 200]
y0 = np.zeros(2 * sys.body_dim * len(sys.body_masses), dtype=np.float64)
x1 = np.array([0.97000436, -0.24308753])
x3p = np.array([-0.93240737, -0.86473146])
y0[0:2] = x1
y0[2:4] = -x1
# y0[4:6] = zero
y0[6:8] = -x3p / 2
y0[8:10] = -x3p / 2
y0[10:12] = x3p
# print(sys.fun(np.zeros_like(y0), y0).reshape(6, -1))
lce, run = solver.get_lce(tspan[1], y0)
t = run['results'].t[1:]
y = run['results'].y[sys.dim:, 1:].reshape(sys.dim, sys.dim, -1)
#print(y[:, :, -1])
lces = []
for i, t_val in enumerate(t):
Df_y = y[:, :, i]
lces.append(solver.calc_lce(Df_y, t_val))
plt.figure()
plt.title(f'LCE ({lces[-1]:.2}) Convergence for 3 Body Figure 8')
plt.plot(t, lces)
plt.ylabel('LCE')
plt.xlabel('t')
plt.savefig(os.path.join(dir_pre, 'lce_converge.png'))
# plt.show(True)
import numpy as np
import os
from echonn.sys import DoublePendulumSystem, SystemSolver
import matplotlib.pyplot as plt
from scipy.constants import pi
if __name__ == "__main__":
sys = DoublePendulumSystem()
slv = SystemSolver(sys)
thetas = np.arange(0.001, pi + 0.0001, pi / 20)
out_img = os.path.join('..', 'images', 'chaos_vs_energy_in_doub_pend.png')
lces = []
for theta in thetas:
lce, _ = slv.get_lce(T=200, y0=[theta, 0, 0, 0])
lces.append(lce)
plt.title('Largest LCE vs Inner Theta IC')
plt.xlabel('Inner Theta')
plt.ylabel('Largest LCE')
plt.plot(180 * thetas / pi, lces)
try:
if os.path.exists(out_img):
os.remove(out_img)
except:
pass # don't worry about it
plt.savefig(out_img)
plt.show(True)
import numpy as np
import matplotlib.pyplot as plt
from echonn.sys import SystemSolver, RestrictedCircular3Body, LyapunovSystem
if __name__ == "__main__":
mu = 0.5
sys = RestrictedCircular3Body(body_ratio=mu)
lce = LyapunovSystem(sys)
#init = [1, -1, .1, .1]
init = np.array(1000 * np.random.rand(4), dtype=int) / 1000
slv = SystemSolver(sys)
#run = slv.run([0, 10], init, max_step=0.001)
T = 100
lce, run = slv.get_lce(T=T, y0=init)
#lce, run = slv.get_lce(T=T)
mat = run['results'].y[4:, -1].reshape(4, 4)
run['results'].y = run['results'].y[[0, 2], :]
slv.plot2d(run)
plt.scatter([-sys.alpha, sys.mu], [0, 0])
print(init)
print(mat)
print('lce:', lce)
#plt.xlim((-15, 15))
#plt.ylim((-15, 15))
# Saved manually since it can't be scripted
plt.show(True)
def testCircleLCE(self):
sys = SystemSolver(CircleSystem())
lce, run = sys.get_lce()
self.assertAlmostEqual(lce, 0, places=4)
def testLCEPendulum(self):
sys = DoublePendulumSystem()
slv = SystemSolver(sys)
slv.get_lce(T=2, y0=[1.8, 1.8, 0, 0])
def runLCETestShort(self, sigma, rho, beta, l1):
sys = LorenzSystem(sigma, rho, beta)
slv = SystemSolver(sys)
slv.get_lce(T=2)