n = 5
h = 1.0/n
K = (1 + h*A)
K.setSym("K")
Y = [Y0]*(n+1)
for i in xrange(n+1):
if i==0:
pass
else:
Y[i] = Y[i-1] * K
Y[i].setSym("Y" + str(i))
P = NDProductDistr([Factor1DDistr(A), Factor1DDistr(Y[0])])
M = Model(P, Y[1:])
M.eliminate_other([K] + Y)
#M2 = M.inference2([Y[0], A], [Y[n]], [1])
#M2.plot(); print M2; show()
#M2 = M.inference2([Y[0]], [Y[n]], [0.5])
#figure()
#M2.plot(); print M2;
figure()
Y[-1].plot(color='r',linewidth=5)
M3 = M.inference([Y[-1]], [], [])
M3.plot(); print M3;
X0 = BetaDistr(2, 2)
y = X0 * exp(A)
y.summary()
Y.append(Y0 * K+ h*U[i])
else:
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))
Y.append(Y0 * K + h * U[i])
else:
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)
Y0 = BetaDistr(2, 2, sym="Y0")
n = 5
h = 1.0 / n
K = (1 + h * A)
K.setSym("K")
Y = [Y0] * (n + 1)
for i in xrange(n + 1):
if i == 0:
pass
else:
Y[i] = Y[i - 1] * K
Y[i].setSym("Y" + str(i))
P = NDProductDistr([Factor1DDistr(A), Factor1DDistr(Y[0])])
M = Model(P, Y[1:])
M.eliminate_other([K] + Y)
#M2 = M.inference2([Y[0], A], [Y[n]], [1])
#M2.plot(); print M2; show()
#M2 = M.inference2([Y[0]], [Y[n]], [0.5])
#figure()
#M2.plot(); print M2;
figure()
Y[-1].plot(color='r', linewidth=5)
M3 = M.inference([Y[-1]], [], [])
M3.plot()
print M3
X0 = BetaDistr(2, 2)
y = X0 * exp(A)
for i in range(n):
print(i)
if i==0:
X[i] = BetaDistr(3, 3, sym = "X0")
Y[i] = BetaDistr(3, 3, sym = "Y0")
else:
X[i] = X[i-1] + h*(A*X[i-1] - B*Y[i-1])
Y[i] = Y[i-1] + h*(-C*X[i-1] + D*Y[i-1])
X[i].setSym("X{}".format(i))
Y[i].setSym("Y{}".format(i))
M = Model([X[0], Y[0], A, B, C, D], X[1:] + Y[1:] )
print(M)
M.eliminate_other([X[0], Y[0], A, B, C, D] + X[1:] + Y[1:])
print(M)
print(Y[1].range())
#M1 = M.inference([X[2], Y[2]], [X[0], Y[0]], [0.5, 0.2])\
figure()
for i in range(n):
M1 = M.inference([X[i], Y[i]], [A, B, C, D], [0.9, 0.2, 0.3, 0.6])
print(M1)
M1.plot(cont_levels=1)
#figure()
#M1.plot(have_3d=True)
show()
h=0.1
for i in range(n):
print i
if i==0:
X[i] = BetaDistr(3, 3, sym = "X0")
Y[i] = BetaDistr(3, 3, sym = "Y0")
else:
X[i] = X[i-1] + h*(A*X[i-1] - B*Y[i-1])
Y[i] = Y[i-1] + h*(-C*X[i-1] + D*Y[i-1])
X[i].setSym("X{}".format(i))
Y[i].setSym("Y{}".format(i))
M = Model([X[0], Y[0], A, B, C, D], X[1:] + Y[1:] )
print M
M.eliminate_other([X[0], Y[0], A, B, C, D] + X[1:] + Y[1:])
print M
print Y[1].range()
#M1 = M.inference([X[2], Y[2]], [X[0], Y[0]], [0.5, 0.2])\
figure()
for i in range(n):
M1 = M.inference([X[i], Y[i]], [A, B, C, D], [0.9, 0.2, 0.3, 0.6])
print M1
M1.plot(cont_levels=1)
#figure()
#M1.plot(have_3d=True)
show()