import numpy as np
from time import time
import sys
sys.path.append('../')
from density_sdsos import compute_reach_picos, compute_reach_mosek
from plot_2d import *
# Initialize symbolic variables
t, x1, x2, d = sp.symbols('t,x1,x2,d')
tmax = 1
data = {'t_var': [t],
'x_vars': [x1, x2],
'd_vars': [],
'maxdeg_rho' : 8,
'rho_0': 0.5 - x1**2 - x2**2,
'vector_field': [t*x2, -x1],
'domain': [2-x1**2, 2-x2**2,t*(tmax-t)],
'tol': 1e-5,
'r': 0}
# (rho, error) = compute_reach_picos(data, solver = 'mosek')
(rho, error) = compute_reach_mosek(data)
print "Density found: rho(t,x1,x2) = ", rho
print "Error:", error
animate([t,x1,x2], [t*x2, -x1], rho, error, 1.1*tmax)
}
plt.figure()
max_deg = 16
min_deg = 6
step = 2
for (i, maxdeg) in enumerate(range(min_deg,max_deg,step)):
print "Solving for degree ", maxdeg
data['maxdeg_rho'] = maxdeg
t0 = time()
(sol, error) = compute_reach_mosek(data)
t1 = time()
print "Solved in ", t1-t0, ", error is ", error
sol_fcn = lambdify([t,x1], sol)
sol_fcn_lower = lambdify([t,x1], sol-t*error)
sol_fcn_upper = lambdify([t,x1], sol+t*error)
T, X = np.mgrid[-0:1:1000j, -1.2:1.2:1000j]
plt.contour(X, T, sol_fcn_upper(T,X), levels=[0.], colors=[plt.get_cmap('autumn', (max_deg-min_deg)/step)(i)] )
plt.contour(X, T, sol_fcn_lower(T,X), levels=[0.], colors=[plt.get_cmap('autumn', (max_deg-min_deg)/step)(i)] )
# plot DE solution
vf = lambdify([t,x1], data['vector_field'])
