def run():
# w, s = sp_odeint(f, w0, t, full_output=True)
w = sp_odeint(f, w0, t)
return w
z0_bar = delta_zi.copy()
z0_bar[:, 0] += x0
z0_bar[:, 1] += v0
normed_delta_zi = np.square(delta_zi)
normed_delta_zi = np.sum(normed_delta_zi, 1)
normed_delta_zi = np.sqrt(normed_delta_zi)
z_lambda_list = list()
for time_interval in T[1:]:
zf_list = list()
t = np.linspace(0, time_interval, 2001)
for z0 in z0_bar:
zf_list.append(sp_odeint(v_, z0, t)[-1])
zf = np.array(zf_list)
normed_zf = zf.copy()
normed_zf[:, 0] = normed_zf[:, 0] - normed_zf[0, 0]
normed_zf[:, 1] = normed_zf[:, 1] - normed_zf[0, 1]
normed_zf = np.square(normed_zf)
normed_zf = np.sum(normed_zf, 1)
normed_zf = np.sqrt(normed_zf)
z_lambda_list.append(np.sum(np.log(normed_zf[1:] / normed_delta_zi[1:])) / ((N - 1) * time_interval))
z_lambda = np.array(z_lambda_list)
plt.plot(z_lambda)
plt.show()
def run(years):
# w, s = sp_odeint(f, w0, t, full_output=True)
w = sp_odeint(f, get_w0(), get_t(years))
return w
def run():
# w, s = sp_odeint(f, w0, t, full_output=True)
w = sp_odeint(f, w0, t)
return w
# wx0 = 50 * (np.random.rand(particle_index) - .5)
# wv0 = 50 * (np.random.rand(particle_index) - .5)
# w0 = np.concatenate([wx0, wv0])
w0 = np.array([], dtype=np.float64)
for x0i, y0i, z0i in zip(x0, y0, z0):
w0 = np.concatenate([w0, [x0i], [y0i], [z0i]])
for vx0i, vy0i, vz0i in zip(vx0, vy0, vz0):
w0 = np.concatenate([w0, [vx0i], [vy0i], [vz0i]])
# w0 = np.array([x0[0], y0[0], z0[0], x0[3], y0[3], z0[3], vx0[0], vy0[0], vz0[0], vx0[3], vy0[3], vz0[3]], dtype=np.float64)
# w0 = np.concatenate([[-10, 0, 0, 10, 0, 0, 0, 10, 0, 0, -10, 0], [0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0]])
# w0 = np.concatenate([[-10, 0, 0, 10, 0, 0], [0, -1, 0, 0, 1, 0]])
t = np.arange(0, time_interval, dt, dtype=np.float64)
w_result = sp_odeint(f, w0, t, mxstep=50000000, hmin=.0001)
trajectories = []
fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection='3d')
# ax.axis('off')
colors = plt.cm.jet(np.linspace(0, 1, number_particles))
lines = sum([ax.plot([], [], [], '.', c=c) for c in colors], [])
lim = 2.0 * earth_distance
ax.set_xlim3d([-lim, lim])
ax.set_ylim3d([-lim, lim])
ax.set_zlim3d([-lim, lim])
time_template = 'time = %.1fdays'
time_text = ax.text(0.05, 0.9, 0.05, '', transform=ax.transAxes)
z0_bar = delta_zi.copy()
z0_bar[:, 0] += x0
z0_bar[:, 1] += v0
normed_delta_zi = np.square(delta_zi)
normed_delta_zi = np.sum(normed_delta_zi, 1)
normed_delta_zi = np.sqrt(normed_delta_zi)
z_lambda_list = list()
for time_interval in T[1:]:
zf_list = list()
t = np.linspace(0, time_interval, 2001)
for z0 in z0_bar:
zf_list.append(sp_odeint(v_, z0, t)[-1])
zf = np.array(zf_list)
normed_zf = zf.copy()
normed_zf[:, 0] = normed_zf[:, 0] - normed_zf[0, 0]
normed_zf[:, 1] = normed_zf[:, 1] - normed_zf[0, 1]
normed_zf = np.square(normed_zf)
normed_zf = np.sum(normed_zf, 1)
normed_zf = np.sqrt(normed_zf)
z_lambda_list.append(
np.sum(np.log(normed_zf[1:] / normed_delta_zi[1:])) /
((N - 1) * time_interval))
z_lambda = np.array(z_lambda_list)
plt.plot(z_lambda)
def generate_double_pend(
batch=1000,
ntotal=500,
nsample=100,
start_theta_1=np.pi / 4,
start_theta_2=np.pi / 4,
stop_t=5, # approximately equal to 6pi
noise_std=.1,
l1=1.,
l2=1.,
m1=1,
m2=1,
g=9.8,
savefig=True):
"""
Args:
batch: batch dimension
ntotal: total number of datapoints per set
nsample: number of sampled datapoints for model fitting
start_theta_1: first arm starting theta value
start_theta_2: second arm starting theta value
stop: ending t value
noise_std: observation noise standard deviation
l1, l2, m1, m2, g: parameters of the double pendulum
savefig: plot the ground truth for sanity check
Returns:
Tuple where first element is true trajectory of size (ntotal, 2),
second element is noisy observations of size (batch, nsample, 2),
third element is timestamps of size (ntotal,),
and fourth element is timestamps of size (nsample,)
"""
y0 = [start_theta_1, start_theta_2, 0.0, 0.0]
orig_ts = np.linspace(0, stop_t, num=ntotal)
samp_ts = orig_ts[:nsample]
sample_plot_range = np.zeros((batch, nsample))
original = sp_odeint(pen_sim.double_pendulum,
y0,
orig_ts,
args=(g, l1, l2, m1, m2))
# remove omega values
original = original[:, 0:2]
samp_trajs = []
for i in range(batch):
# don't sample t0 very near the start or the end
t0_idx = npr.randint(0, ntotal - nsample)
sample_plot_range[i, :] = orig_ts[t0_idx:t0_idx + nsample]
samp_traj = original[t0_idx:t0_idx + nsample, :].copy()
samp_traj += npr.randn(*samp_traj.shape) * noise_std
samp_trajs.append(samp_traj)
samp_trajs = np.stack(samp_trajs, axis=0)
return original, samp_trajs, orig_ts, samp_ts, sample_plot_range
# wx0 = 50 * (np.random.rand(particle_index) - .5)
# wv0 = 50 * (np.random.rand(particle_index) - .5)
# w0 = np.concatenate([wx0, wv0])
w0 = np.array([], dtype=np.float64)
for x0i, y0i, z0i in zip(x0, y0, z0):
w0 = np.concatenate([w0, [x0i], [y0i], [z0i]])
for vx0i, vy0i, vz0i in zip(vx0, vy0, vz0):
w0 = np.concatenate([w0, [vx0i], [vy0i], [vz0i]])
# w0 = np.array([x0[0], y0[0], z0[0], x0[3], y0[3], z0[3], vx0[0], vy0[0], vz0[0], vx0[3], vy0[3], vz0[3]], dtype=np.float64)
# w0 = np.concatenate([[-10, 0, 0, 10, 0, 0, 0, 10, 0, 0, -10, 0], [0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0]])
# w0 = np.concatenate([[-10, 0, 0, 10, 0, 0], [0, -1, 0, 0, 1, 0]])
t = np.arange(0, time_interval, dt, dtype=np.float64)
w_result = sp_odeint(f, w0, t, mxstep=50000000, hmin=.0001)
trajectories = []
fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection='3d')
# ax.axis('off')
colors = plt.cm.jet(np.linspace(0, 1, number_particles))
lines = sum([ax.plot([], [], [], '.', c=c) for c in colors], [])
lim = 2.0 * earth_distance
ax.set_xlim3d([-lim, lim])
ax.set_ylim3d([-lim, lim])
ax.set_zlim3d([-lim, lim])
time_template = 'time = %.1fdays'
time_text = ax.text(0.05, 0.9, 0.05, '', transform=ax.transAxes)
def run(years):
# w, s = sp_odeint(f, w0, t, full_output=True)
w = sp_odeint(f, get_w0(), get_t(years))
return w
import sympy as sp
import numpy as np
import matplotlib.pylab as plt
sp.init_printing()
from scipy.integrate import odeint as sp_odeint
def v_(z, t):
return np.array([z[1], -np.sin(z[0]) - np.sin(z[0] - 2 * t)])
ti = 0
tf = 200
dt = .1
xi_vi = [-.5, 0]
t2 = np.linspace(ti, tf, 20001)
t1 = np.linspace(ti, tf, 2001)
x1_v1 = sp_odeint(v_, xi_vi, t1)
x2_v2 = sp_odeint(v_, xi_vi, t2)
plt.plot(t2, x2_v2)
plt.plot(t1, x1_v1)
plt.show()
