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 evalLL(self, HObj, Pst):
try:
val = 0.
for i in range(self.data.shape[0] - 1):
J = HJacobi_integrator(HObj, Pst)
pT = pTransition(J)
pT.make(self.data[i], self.tt)
val += -np.log(pT(self.data[i + 1]))
return val
except:
return np.inf
def evalLL_wrep(self, HObj, Pst):
try:
val = 0.
for i, R in zip(self.repData.inds, self.repData.Ireps):
# Make Pt for i
J = HJacobi_integrator(HObj, Pst)
pT = pTransition(J)
pT.make(self.data[i], self.tt)
for j in R:
if j != (self.data.shape[0] - 1):
val += np.log(pT(self.data[j + 1]))
return -val
except:
return np.inf
def ObjFunc(par):
# Create a new add_term for the Hamiltonian object
def func(x, p):
return par * (p - H.seperatrix(x))**2
H.set_add_term(func)
# Make transition PDF
try:
# Do something
H.set_add_term(func)
J = HJacobi_integrator(H, Pst)
pT_1 = pTransition(J)
pT_1.make(x0, tt)
l = np.log(pT_1(R[:, -1]))
return -np.sum(l)
except:
# Do something else
return np.inf
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
res = minimize(ObjFunc, 0.1, method='Nelder-Mead')
print res
#class ares:
# def __init__(self):
# self.x = 0.07539063
#res = ares()
def func(x, p):
return res.x * (p - H.seperatrix(x))**2
H.set_add_term(func)
J = HJacobi_integrator(H, Pst)
pT = pTransition(J)
pT.make(x0, tt)
xx = np.linspace(-1.5, 1.5, 500)
fig2 = plt.figure()
ax = fig2.add_subplot(111)
ax.plot(xx, pT(xx))
from sklearn import mixture
clf = mixture.GaussianMixture(n_components=3, covariance_type='full')
clf.fit(R[:, -1].reshape(NSim, 1))
p = np.zeros(xx.size)
print clf.means_
print clf.covariances_
J = HJacobi_integrator(H, Pst)
from scipy.integrate import odeint
from scipy.misc import derivative
x0 = 0.1
print derivative(lambda x: fgrad(x), x0=x0, dx=1e-6)
def dXdt(X, t=0):
v = -fgrad(X[0])
return np.array([v])
mode = odeint(dXdt, x0, np.linspace(0., T, 1000))
print "The mode is: ", mode[-1], np.sqrt(par)
pT1 = pTransition(J)
pT1.make(x0, tt)
intPar = integrator_pars(delta=[0.3, 0.3], scale=1.5, dxTarget=0.01)
pT2 = pTransition2(H, intPar)
pT2.make(x0, T)
xx = np.linspace(-1.5, 1.5, 1000)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xx, pT1(xx), 'b-')
ax.plot(xx, pT2(xx), 'r-')
plt.show()
H = Hamiltonian(U,lambda x: 0.5) Pst = pStationary(H) J = HJacobi_integrator(H,Pst) Jt_1 = J(tt,J0f) from JIntegrator import integrator_pars """ """ xx = J.xx fig = plt.figure() ax = fig.add_subplot(111) pT_1 = pTransition(J) pT_1.make(x0,tt) intPar = integrator_pars(delta=[0.3,0.3],scale=1.25,dxTarget=0.005) pT_2 = pTransition2(H,intPar) pT_2.make(x0,T) #ax.plot(xx,pT_1(xx),'b-') ax.plot(xx,pT_2(xx)) for eps in [0.03,0.04,0.05,0.06] : def func(x,p): return eps*(p-H.seperatrix(x))**2 print eps try: H.set_add_term(func)