#show()
#A = UniformDistr(0,1, sym = "A")
#B = UniformDistr(0,1, sym = "B")
for i in range(n):
print "X{}".format(i)
X[i] = BetaDistr(2, 2, sym = "X{}".format(i))
if i==0:
S[i] = X[0]
else:
S[i] = S[i-1] + X[i]
S[i].setSym("S{}".format(i))
M = Model(X, S[1:])
print M
M.toGraphwiz()
#M = M.inference([S[-1], S[-4]], [S[-3]], [1])
#M = M.inference([X[0], X[1]], [S[-1]], [3.5])
print "===================="
M1 = M.inference(wanted_rvs =[X[0], X[1]], cond_rvs=[S[-1]], cond_X=[1])
print "====================",M1
M2 = M.inference(wanted_rvs =[S[1], S[4]])
print "====================",M2
M3 = M.inference(wanted_rvs =[S[1], S[4]], cond_rvs=[S[3]], cond_X=[2])
print "====================",M3
MC_X0 = M.inference(wanted_rvs =[X[0]], cond_rvs=[S[-1]], cond_X=[1])
print "===================="
print M1
figure()
M1.plot(cont_levels=10)
Y.append(Y[i-1] * K+ h*U[i])
Y[-1].setSym("Y" + str(i+1))
ei = NormalDistr(0.0, 0.1) | Between(-0.4, 0.4)
ei.setSym("E{0}".format(i))
E.append(ei)
O.append(Y[-1] + E[-1])
O[-1].setSym("O{0}".format(i))
#!
#! Model
#! -----
P = NDProductDistr([A, Y0] + E + U)
M = Model(P, O)
print M
M.eliminate_other(E + Y + O + [A, Y0] + U)
print M
M.toGraphwiz(f=open('bn.dot', mode="w+"))
#!
#! Joint distribution of initial condition and parameter of equation
#! -----------------------------------------------------------------
i = 0
ay0 = []
ui = [0.0]*n
figure()
for yend in [0.25, 1.25, 2.25]:
M2 = M.inference(wanted_rvs=[A, Y0], cond_rvs=[O[-1]] + U, cond_X=[yend] + ui)
subplot(1, 3, i + 1)
title("O_{0}={1}".format(n, yend))
M2.plot()
ay0.append(M2.nddistr.mode()) # "most probable" state
#show()
#A = UniformDistr(0,1, sym = "A")
#B = UniformDistr(0,1, sym = "B")
for i in range(n):
print("X{}".format(i))
X[i] = BetaDistr(2, 2, sym = "X{}".format(i))
if i==0:
S[i] = X[0]
else:
S[i] = S[i-1] + X[i]
S[i].setSym("S{}".format(i))
M = Model(X, S[1:])
print(M)
M.toGraphwiz()
#M = M.inference([S[-1], S[-4]], [S[-3]], [1])
#M = M.inference([X[0], X[1]], [S[-1]], [3.5])
print("====================")
M1 = M.inference(wanted_rvs =[X[0], X[1]], cond_rvs=[S[-1]], cond_X=[1])
print("====================",M1)
M2 = M.inference(wanted_rvs =[S[1], S[4]])
print("====================",M2)
M3 = M.inference(wanted_rvs =[S[1], S[4]], cond_rvs=[S[3]], cond_X=[2])
print("====================",M3)
MC_X0 = M.inference(wanted_rvs =[X[0]], cond_rvs=[S[-1]], cond_X=[1])
print("====================")
print(M1)
figure()
M1.plot(cont_levels=10)
Y.append(Y[i - 1] * K + h * U[i])
Y[-1].setSym("Y" + str(i + 1))
ei = NormalDistr(0.0, 0.1) | Between(-0.4, 0.4)
ei.setSym("E{0}".format(i))
E.append(ei)
O.append(Y[-1] + E[-1])
O[-1].setSym("O{0}".format(i))
#!
#! Model
#! -----
P = NDProductDistr([A, Y0] + E + U)
M = Model(P, O)
print M
M.eliminate_other(E + Y + O + [A, Y0] + U)
print M
M.toGraphwiz(f=open('bn.dot', mode="w+"))
#!
#! Joint distribution of initial condition and parameter of equation
#! -----------------------------------------------------------------
i = 0
ay0 = []
ui = [0.0] * n
figure()
for yend in [0.25, 1.25, 2.25]:
M2 = M.inference(wanted_rvs=[A, Y0],
cond_rvs=[O[-1]] + U,
cond_X=[yend] + ui)
subplot(1, 3, i + 1)
title("O_{0}={1}".format(n, yend))
for i in range(n):
U.append(UniformDistr(-0.2, 0.2, sym="U{0}".format(i)))
if i == 0:
Y.append(Y0 * K + U[i])
else:
Y.append(Y[i - 1] * K + U[i])
Y[i].setSym("Y" + str(i + 1))
ei = NormalDistr(0.05, 0.1) | Between(-0.4, 0.4)
ei.setSym("E{0}".format(i))
E.append(ei)
O.append(Y[-1] + E[-1])
O[-1].setSym("O{0}".format(i))
# print O[-1].range(), O[-1].range_()
M = Model(U + [Y0] + E, Y + O)
print(M)
M.toGraphwiz(f=open("bn.dot", mode="w+"))
#!
#! Simulation with signal filtering
#! --------------------------------
nT = 100
u = zeros(nT)
t = zeros(nT)
Yorg = zeros(nT)
Ynoised = zeros(nT)
Ydenoised = zeros(nT)
Udenoised = zeros(nT)
yi = 0.0
ydenoise = 0.0
ynoise = 0.0
y = 0.0
figure()