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()