).satisfiability_report()
print Proposition(
lambda a, b, c: (implies(a, b) or implies(b, c)) == implies(a, c),
"((a => b) and (b => c)) == (a => c)"
).satisfiability_report()
print "\n=== Problem 14 ==="
from MDP.grid import GridWorld
GRID = [[0, 0, None, 100],
[0, 0, 0, 0]]
PROB = {
'S':(('S', 1.0), ),
'N':(('N', 1.0), ),
'E':(('E', 1.0), ),
'W':(('W', 1.0), ),
}
STATES = ((1,3),(1,2),(1,1),(0,1),(1,0),(0,0))
g = GridWorld(GRID, PROB, STATES, 1, -5)
i = g.value_iteration(0.1)
print "Values after %d iterations:" % i
print g
print "\n=== Problem 15 ==="
from Markov.markov import TransProb
TRANSITIONS = [("A","A","A","A","B")]
t = TransProb(TRANSITIONS)
t.report(k=1)
from Markov.markov import TransProb, MarkovChain, MarkovModel
print "\n=== Homework 6.1 ==="
OBSERVATIONS = (("A", "B", "C", "A", "B", "C"), ("A", "A", "B", "B", "C", "C"),
("A", "A", "A", "C", "C", "C"))
t = TransProb(OBSERVATIONS)
t.report()
print "\n=== Homework 6.2 ==="
CHAIN = ("A", 1.0, {True: 0.9, False: 0.5})
c = MarkovChain(CHAIN)
print "stationary distribution: P(A) = %.4f" % c.stationary_distribution(True)
print "stationary distribution: P(B) = %.4f" % c.stationary_distribution(False)
print "\n=== Homework 6.3 ==="
MODEL = ("A", 0.5, {True: 0.5, False: 0.5}, "X", {True: 0.1, False: 0.8})
m = MarkovModel(MODEL)
m.p({"A0": True}, {"X0": True})
m.p({"A1": True}, {"X0": True})
m.p({"A1": True}, {"X0": True, "X1": True})
print "\n=== Homework 6.11 ==="
from Game.game import Game
HW6_11 = {
"players": (("B", "d", "e", "f"), ("A", "a", "b", "c")),
"matrix": (
((3, 3), (5, 0), (2, 1)),
((2, 4), (7, 8), (4, 6)),
((7, 5), (8, 5), (5, 3)),
)
}
c.p({"R1":True})
c.p({"R2":True})
c.p({"R3":True})
print "stationary distribution: P(R) = %.4f" % c.stationary_distribution()
print "\nA Example"
A_CHAIN = ("A", 1.0, {True: 0.5, False: 1.0})
c = MarkovChain(A_CHAIN, 3)
c.p({"A1":True})
c.p({"A2":True})
c.p({"A3":True})
print "stationary distribution: P(A) = %.4f" % c.stationary_distribution()
print "\nTransition Probabilities 1"
TRANSITIONS = [("R","S","S","S","R","S","R")]
t = TransProb(TRANSITIONS)
t.report()
print "\nTransition Probabilities 2"
TRANSITIONS = [("S","S","S","S","S","R","S","S","S","R","R")]
t = TransProb(TRANSITIONS)
t.report()
print "\nTransition Probabilities 3"
TRANSITIONS = [("R","S","S","S","S")]
t = TransProb(TRANSITIONS)
t.report(k=1)
print "\nMarkov Model 1"
MODEL = ("R", 0.5, {True: 0.6, False: 0.2}, "H", {True: 0.4, False: 0.9})
m = MarkovModel(MODEL)
from Markov.markov import TransProb, MarkovChain, MarkovModel
print "\n=== Homework 6.1 ==="
OBSERVATIONS = (
("A", "B", "C", "A", "B", "C"),
("A", "A", "B", "B", "C", "C"),
("A", "A", "A", "C", "C", "C")
)
t = TransProb(OBSERVATIONS)
t.report()
print "\n=== Homework 6.2 ==="
CHAIN = ("A", 1.0, {True: 0.9, False: 0.5})
c = MarkovChain(CHAIN)
print "stationary distribution: P(A) = %.4f" % c.stationary_distribution(True)
print "stationary distribution: P(B) = %.4f" % c.stationary_distribution(False)
print "\n=== Homework 6.3 ==="
MODEL = ("A", 0.5, {True: 0.5, False: 0.5}, "X", {True: 0.1, False: 0.8})
m = MarkovModel(MODEL)
m.p({"A0":True}, {"X0":True})
m.p({"A1":True}, {"X0":True})
m.p({"A1":True}, {"X0":True, "X1":True})
print "\n=== Homework 6.11 ==="
from Game.game import Game
HW6_11 = {
"players": (
("B", "d", "e", "f"),
("A", "a", "b", "c")
),