In [7]:

    

import sklearn
import numpy as np
from numpy import linalg as LA
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import seaborn as sb
%matplotlib inline


    

In [301]:

    

Nrealiz = 50

Nt = 200
T = 20
t_ = np.linspace(0,T,Nt) # time grid

K = 10   ## omega0 = sqrt(k/m)
C = 0.2
sigk = 2.0
sigc = 0.0

# state: u = [x, xdot]
x0 = 1
xdot0 = 0.0
#u0 = np.array([x0,xdot0]) # initial condition


    

In [304]:

    

def lin_damp_osc_stoch(k0,c0,x0,xdot0,sigk,sigc,t_):
    def randn1(mu,sig,N):
        return mu + sig*np.random.randn(N)
    def randu1(mu,sig,N):
        return mu + sig*(np.random.rand(N) -1/2)
    k = randu1(k0,sigk,1)
    c = randu1(c0,sigc,1)
    A = np.array([[0,1],[-k,-c]]) # system mtx
    def f(u,t):
        return A.dot(u)
    soln = odeint(f, u0, t_)
    xpos = soln[:, 0]
    xvel = soln[:, 1]
    return xpos


    

In [305]:

    

xpos = [lin_damp_osc_stoch(K,C,x0,xdot0,sigk,sigc,t_) for _ in range(Nrealiz)]

#xpos = x[:,1]
# plt.figure()
# ax = plt.subplot(111)

cis = np.linspace(95,10,4)
# sb.tsplot(xpos,t_, err_style="ci_band", ci=cis)
# sb.tsplot(xpos, t_, estimator=np.mean, err_style='unit_traces')
sb.set_style("white")
sb.tsplot(xpos, t_, estimator=np.mean, err_style='unit_traces', color="muted", linewidth=0, err_kws={"alpha": .05})

plt.plot(t_,xpos[2],'r')

# sb.tsplot(xpos, err_style='ci_bars')
# plt.figure()
# plt.plot(t_,xpos[2])


    

    
Out[305]:





[<matplotlib.lines.Line2D at 0x111558450>]






    

In [ ]:

    

np.std