def objFunc(par):
# Set up the necessary functions
def f(x):
return -(-x**4 + 2 * par * x**2)
def fgrad(x):
return -(4 * x * (par - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
eps = 0.0
def func(x, p):
return eps * (p - H.seperatrix(x))**2
H.set_add_term(func)
Pst = None
rootPar = np.sqrt(par)
#xRep = [-0.63,0.63]
xRep = [z[20], z[-20]]
try:
val = 0.
J = HJacobi_integrator(H, Pst)
pT1 = pTransition(J)
pT1.make(xRep[0], tt)
pT2 = pTransition(J)
pT2.make(xRep[1], tt)
xx = J.xx
"""
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xx,pT1(xx))
ax.plot(xx,pT2(xx))
"""
val = 0.
for i in range(X.size - 1):
x = X[i]
xT = X[i + 1]
if x < xRep[0]:
val += np.log(pT1(xT))
elif x > xRep[1]:
val += np.log(pT2(xT))
else:
w = abs(x - xRep[0]) / (xRep[1] - xRep[0])
val += np.log(w * pT1(xT) + (1 - w) * pT2(xT))
return -val
except:
return np.inf
def test():
import numpy as np
from main import init_dbw_example, potential, Hamiltonian, pStationary, HJacobi_integrator
from main import pTransition
from scipy.integrate import odeint
from scipy.interpolate import UnivariateSpline
x0 = 0.3
T = 0.5
par = 0.8
D2 = .5
def f(x):
return -(-x**4 + 2 * par * x**2)
def fgrad(x):
return -(4 * x * (par - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
Pst = None
J = HJacobi_integrator(H, Pst)
def J0f(x):
return 10 * (x - x0)**2
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
def dJdt(J, t=0, xx=[1., 0.]):
dx = xx[1] - xx[0]
dJdx = np.gradient(J, dx)
return -H(xx, dJdx)
def objFuncMF(par):
# Set up the necessary functions
def f(x):
return -(-x**4 + 2 * par * x**2)
def fgrad(x):
return -(4 * x * (par - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
Pst = pStationary(H)
return -np.sum(np.log(Pst(X)))
def __call__(self, par, delT):
self.tt = np.linspace(0., delT, 100)
D2 = np.exp(par[1])
def f(x):
return -(-x**4 + 2 * par[0] * x**2)
def fgrad(x):
return -(4 * x * (par[0] - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
Pst = None
if self.has_repr:
return self.evalLL_wrep(H, Pst)
else:
return self.evalLL(H, Pst)
def makeH():
import numpy as np
from main import init_dbw_example, potential, Hamiltonian, pStationary, HJacobi_integrator
from main import pTransition
from scipy.integrate import odeint
from scipy.interpolate import UnivariateSpline
x0 = 0.3
T = 0.5
par = 0.8
D2 = .5
def f(x):
return -(-x**4 + 2 * par * x**2)
def fgrad(x):
return -(4 * x * (par - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
return H
def objFunc(par):
# Set up the necessary functions
def f(x):
return -(-x**4 + 2 * par * x**2)
def fgrad(x):
return -(4 * x * (par - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
Pst = None
try:
val = 0.
for i in range(X.size - 1):
J = HJacobi_integrator(H, Pst)
pT = pTransition(J)
pT.make(X[i], tt)
val += -np.log(pT(X[i + 1]))
return val
except:
return np.inf
return np.mean(X), np.var(X)
f, fg = init_dbw_example()
U = potential(f, fg)
x0 = 0.4
T = 0.5
tt = np.linspace(0., T, 100)
def J0f(x):
return 100 * (x - x0)**2
H = Hamiltonian(U, lambda x: 0.5)
Pst = pStationary(H)
dX = Diffusion(H)
NSim = 100
n = 500
rSample = np.zeros(NSim)
# R
# - Costly, used for plotting purposes
R = np.zeros((NSim, n))
# 35878
seed = np.random.choice(range(100000))
print seed
T = 0.5
par = 0.8
D2 = .5
def f(x):
return -(-x**4 + 2 * par * x**2)
def fgrad(x):
return -(4 * x * (par - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
Pst = None
J = HJacobi_integrator(H, Pst)
def J0f(x):
return 10 * (x - x0)**2
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
def dJdt(J, t=0, xx=None, dx=1.):
dJdx = np.gradient(J, dx)
D2 = .5
par = .8
def f(x):
return -(-x**4 + 2 * par * x**2)
def fgrad(x):
return -(4 * x * (par - x**2))
U = potential(f, fgrad)
H = Hamiltonian(U, lambda x: D2)
def exp_cdf(t, l=1.3):
return 1 - np.exp(-l * t)
x0 = 1.3
t = 0.
T = .8
from scipy.integrate import quad
JT1, xx = get_Jt(0.8, T, H, exp_cdf)
JT2, _ = get_Jt(-0.03, T, H, exp_cdf)
JT3, _ = get_Jt(-0.8, T, H, exp_cdf)
import numpy as np import matplotlib.pyplot as plt from main import init_dbw_example,potential,Hamiltonian,pStationary,HJacobi_integrator from scipy.interpolate import UnivariateSpline """ Investigating properties of the homotopy method """ f,fg = init_dbw_example() U = potential(f,fg) H = Hamiltonian(U,lambda x: 0.5) Pst = pStationary(H) J = HJacobi_integrator(H,Pst) x0 = 0.3 T = 0.3 tt = np.linspace(0.,T,100) Jt = J(tt,lambda x : 10*(x-x0)**2) xx = J.xx dx = J.dx """ Plot the gradient over the contours of the Hamiltonian """ fig = plt.figure() ax = fig.add_subplot(111) # Smooth the oscillations
s = self.sim(x0, T, n)
X[i] = s[-1]
if withMix:
from sklearn import mixture
clf = mixture.GaussianMixture(n_components=2,
covariance_type='full')
clf.fit(X.reshape(nSim, 1))
return np.mean(X), np.var(X), clf
else:
return np.mean(X), np.var(X)
f, fg = init_dbw_example()
U = potential(f, fg)
H = Hamiltonian(U, lambda x: 1.)
Pst = pStationary(H)
dX = Diffusion(H)
NSim = 100
T = 0.5
rSample = np.zeros(NSim)
x0 = 0.1
tt = [0.]
rSample[0] = x0
t = 0.
seed = np.random.choice(range(100))
from main import pTransition, pTransition2 from JIntegrator import integrator_pars from scipy.interpolate import UnivariateSpline from scipy.integrate import odeint import matplotlib.pyplot as plt D2 = .5 par = .8 def f(x): return -(-x**4 + 2*par*x**2) def fgrad(x): return -(4*x*(par-x**2)) U = potential(f,fgrad) H = Hamiltonian(U,lambda x: D2) def exp_cdf(t,l = 1.3): return 1-np.exp(-l*t) x0 = 0.8 t = 0. T = .1 fig = plt.figure() ax = fig.add_subplot(111) for i in range(10) : tt = np.linspace(t,t+T,1000) J = HJacobi_integrator(H,None)