def write_image(k):
q,p,mu,q1 = jpf.state_to_weinstein_darboux( y_data[k] )
f = gf.display_velocity(q,p,mu)
time_s = str(time_data[k])
plt.suptitle('t = '+ time_s[0:4] , fontsize=16 , x = 0.75 , y = 0.25 )
fname = './movie_frames/frame_%03i.png' % k
f.savefig( fname )
plt.close(f)
sys.stdout.write(' '+str(k))
sys.stdout.flush()
def write_image(k):
q, p, mu, q1 = jpf.state_to_weinstein_darboux(y_data[k])
f = gf.display_velocity(q, p, mu)
time_s = str(time_data[k])
plt.suptitle('t = ' + time_s[0:4], fontsize=16, x=0.75, y=0.25)
fname = './movie_frames/frame_%03i.png' % k
f.savefig(fname)
plt.close(f)
sys.stdout.write(' ' + str(k))
sys.stdout.flush()
spin = np.array([[0., -1.], [1., 0.]])
stretch = np.array([[1., 0.], [0., -1.]])
shear = np.array([[0., 1.], [0., 0.]])
q = np.random.rand(N, DIM)
#p = np.zeros([N,DIM])
p = np.random.rand(N, DIM)
mu = np.random.rand(N, DIM, DIM)
#mu[0] = 0.5*spin
#mu[1] = -0.5*spin
#mu[0] = np.load('mu.npy')
#p = -q*np.ones([N,DIM])
#mu = np.random.randn(N,DIM,DIM)
#for i in range(0,N):
# mu[i] = mu[i] - np.mean(np.diag(mu[i]))*np.eye(DIM)
#print 'testing various functions'
#print jpf.test_functions(1)
print 'initial energy is ' + str(jpf.Hamiltonian(q, p, mu))
state = jpf.weinstein_darboux_to_state(q, p, mu)
step_max = 100
t_span = np.linspace(0., 4.0, step_max)
y_span = odeint(jpf.ode_function, state, t_span, rtol=0.000001)
np.save('state_data', y_span)
np.save('time_data', t_span)
q, p, mu = jpf.state_to_weinstein_darboux(y_span[step_max - 1])
print 'final energy is ' + str(jpf.Hamiltonian(q, p, mu))
print 'initial momentum: %.3f,%.3f %.3f' % ( pi[0], pi[1], Li[0][1] )
print 'initial J_R^1 momenta:'
Ki = np.zeros([N,DIM,DIM])
for i in range(0,N):
Ki[i] = jpf.Jr1_momentum(q,p,mu,q1,particles=[i])
print Ki[i]
state = jpf.weinstein_darboux_to_state( q , p , mu , q1 )
step_max = 406
t_span = np.linspace( 0. , T , step_max )
y_span = odeint( jpf.ode_function , state , t_span , rtol=0.0000001 )
np.save('state_data',y_span)
np.save('time_data',t_span)
q,p,mu,q1 = jpf.state_to_weinstein_darboux( y_span[step_max-1] )
Ef = jpf.Hamiltonian(q,p,mu)
pf = jpf.lin_momentum(q,p,mu)
Lf = jpf.ang_momentum(q,p,mu)
print ' final energy: %.3f diff = %.3e' % ( Ef, Ef-Ei )
print ' final momentum: %.3f,%.3f %.3f diff = %.3e %.3e' % \
( pf[0], pf[1], Lf[0][1], np.linalg.norm(pf-pi), np.fabs(Lf[0][1]-Li[0][1]) )
print ' final position: %.2f,%.2f' % ( q[0][0], q[0][1] )
print 'dist = %.3e p_0 = %.3e' % ( np.linalg.norm(q[1]-q[0]), np.linalg.norm(p[0]) )
print ' final J_R^1 momenta:'
Kf = np.zeros([N,DIM,DIM])
for i in range(0,N):
Kf[i] = jpf.Jr1_momentum(q,p,mu,q1,particles=[i])
print Kf[i]
import matplotlib.pyplot as plt
import numpy as np
import sys
N = jpf.N
DIM = jpf.DIM
SIGMA = jpf.SIGMA
y_data = np.load('./state_data.npy')
times = np.load('./time_data.npy')
N_timestep = y_data.shape[0]
momenta = np.zeros([N, 3, N_timestep])
for i in range(N_timestep):
q, p, mu, q1 = jpf.state_to_weinstein_darboux(y_data[i])
for j in range(N):
tmp = jpf.lin_momentum(q, p, mu, [j])
momenta[j][0][i] = tmp[0]
momenta[j][1][i] = tmp[1]
momenta[j][2][i] = jpf.ang_momentum(q, p, mu, [j])[0][1]
plt.figure()
plt.xlabel('t')
plt.plot(times, momenta[0][2], 'b-', times, momenta[1][2], 'r-', times,
momenta[2][2], 'g-')
#plt.axis([0,times[N_timestep-1],0,1])
plt.show()
import numpy as np
import sys
N = jpf.N
DIM = jpf.DIM
SIGMA = jpf.SIGMA
y_data = np.load('./state_data.npy')
times = np.load('./time_data.npy')
N_timestep = y_data.shape[0]
momenta = np.zeros([N,3,N_timestep])
for i in range(N_timestep):
q,p,mu,q1 = jpf.state_to_weinstein_darboux( y_data[i] )
for j in range(N):
tmp = jpf.lin_momentum(q,p,mu,[j])
momenta[j][0][i] = tmp[0]
momenta[j][1][i] = tmp[1]
momenta[j][2][i] = jpf.ang_momentum(q,p,mu,[j])[0][1]
plt.figure()
plt.xlabel('t')
plt.plot(times,momenta[0][2],'b-',
times,momenta[1][2],'r-',
times,momenta[2][2],'g-')
#plt.axis([0,times[N_timestep-1],0,1])
plt.show()