Localization.py

## Modify the empty list, p, so that it becomes a UNIFORM probability
# distribution over five grid cells, as expressed in a list of
# five probabilities.

p = [0.2,0.2,0.2,0.2,0.2]

print p   # TRUE

## Modify your code to create probability vectors, p, of arbitrary
# size, n. Use n=5 to verify that your new solution matches
# the previous one.

p=[]
n=5

print p  # [0.2,0.2,0.2,0.2,0.2] should be

## Write code that outputs p after multiplying each entry
#by pHit or pMiss at the appropriate places. Remember that
#the red cells 1 and 2 are hits and the other green cells
#are misses.


p=[0.2,0.2,0.2,0.2,0.2]
pHit = 0.6
pMiss = 0.2

#Enter code here
p = []

print p

## Modify the program to find and print the sum of all the entries in the list p.

p=[0.2, 0.2, 0.2, 0.2, 0.2]
pHit = 0.6
pMiss = 0.2

p[0]=p[0]*pMiss
p[1]=p[1]*pHit
p[2]=p[2]*pHit
p[3]=p[3]*pMiss
p[4]=p[4]*pMiss

# Enter your code below
print(sum(p)) # TRUE

## Modify the code below so that the function sense, which
#takes p and Z as inputs, will output the NON-normalized
#probability distribution, q, after multiplying the entries
#in p by pHit or pMiss according to the color in the
#corresponding cell in world.

p=[0.2, 0.2, 0.2, 0.2, 0.2]
world=['green', 'red', 'red', 'green', 'green']
Z = 'red'
pHit = 0.6
pMiss = 0.2

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    return q

print sense(p,Z) # TRUE

## Modify your code so that it normalizes the output for
#the function sense. This means that the entries in q
#should sum to one.

p=[0.2, 0.2, 0.2, 0.2, 0.2]
world=['green', 'red', 'red', 'green', 'green']
Z = 'red'
pHit = 0.6
pMiss = 0.2

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    s = sum(q)
    for i in range(len(p)):
        q[i]=q[i]/s
    return q
print sense(p,Z) # TRUE

## Try using your code with a measurement of 'green' and
#make sure the resulting probability distribution is correct.

p=[0.2, 0.2, 0.2, 0.2, 0.2]
world=['green', 'red', 'red', 'green', 'green']
Z = 'green'
pHit = 0.6
pMiss = 0.2

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    s = sum(q)
    for i in range(len(p)):
        q[i]=q[i]/s
    return q
print sense(p, Z) # TRUE

#Modify the code so that it updates the probability twice
#and gives the posterior distribution after both
#measurements are incorporated. Make sure that your code
#allows for any sequence of measurement of any length.

p=[0.2, 0.2, 0.2, 0.2, 0.2]
world=['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'green']
pHit = 0.6
pMiss = 0.2

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    s = sum(q)
    for i in range(len(q)):
        q[i] = q[i] / s
    return q
#
#ADD YOUR CODE HERE
#
print p

## Program a function that returns a new distribution
#q, shifted to the right by U units. If U=0, q should
#be the same as p.

p=[0, 1, 0, 0, 0]
world=['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'green']
pHit = 0.6
pMiss = 0.2

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    s = sum(q)
    for i in range(len(q)):
        q[i] = q[i] / s
    return q

def move(p, U):
    #
    U = U % len(p)
    q = p[-U:] + p[:-U]
    #
    return q

print move(p, 1) # TRUE


## Modify the move function to accommodate the added
# probabilities of overshooting or undershooting
# the intended destination.

p = [0, 1, 0, 0, 0]
world = ['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'green']
pHit = 0.6
pMiss = 0.2
pExact = 0.8
pOvershoot = 0.1
pUndershoot = 0.1


def sense(p, Z):
    q = []
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1 - hit) * pMiss))
    s = sum(q)
    for i in range(len(q)):
        q[i] = q[i] / s
    return q


def move(p, U):
    q = []
    for i in range(len(p)):
        s = pExact * p[(i-U) % len(p)]
        s = s + pOvershoot * p[(i-U-1) % len(p)]
        s = s + pUndershoot * p[(i-U+1) % len(p)]
        q.append(s)
    return q

print move(p, 1) # TRUE


## Write code that makes the robot move twice and then prints
# out the resulting distribution, starting with the initial
# distribution p = [0, 1, 0, 0, 0]

p=[0, 1, 0, 0, 0]
world=['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'green']
pHit = 0.6
pMiss = 0.2
pExact = 0.8
pOvershoot = 0.1
pUndershoot = 0.1

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    s = sum(q)
    for i in range(len(q)):
        q[i] = q[i] / s
    return q

def move(p, U):
    q = []
    for i in range(len(p)):
        s = pExact * p[(i-U) % len(p)]
        s = s + pOvershoot * p[(i-U-1) % len(p)]
        s = s + pUndershoot * p[(i-U+1) % len(p)]
        q.append(s)
    return q
#
p = move(p,1)
p = move(p,1)
print p # TRUE


## Write code that moves 1000 times and then prints the
#resulting probability distribution.

p=[0, 1, 0, 0, 0]
world=['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'green']
pHit = 0.6
pMiss = 0.2
pExact = 0.8
pOvershoot = 0.1
pUndershoot = 0.1

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    s = sum(q)
    for i in range(len(q)):
        q[i] = q[i] / s
    return q

def move(p, U):
    q = []
    for i in range(len(p)):
        s = pExact * p[(i-U) % len(p)]
        s = s + pOvershoot * p[(i-U-1) % len(p)]
        s = s + pUndershoot * p[(i-U+1) % len(p)]
        q.append(s)
    return q
#
for i in range(100):
    p = move(p,1)
#
print p # TRUE


## Given the list motions=[1,1] which means the robot
#moves right and then right again, compute the posterior
#distribution if the robot first senses red, then moves
#right one, then senses green, then moves right again,
#starting with a uniform prior distribution.

p=[0.2, 0.2, 0.2, 0.2, 0.2]
world=['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'green']
motions = [1,1]
pHit = 0.6
pMiss = 0.2
pExact = 0.8
pOvershoot = 0.1
pUndershoot = 0.1

def sense(p, Z):
    q=[]
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
    s = sum(q)
    for i in range(len(q)):
        q[i] = q[i] / s
    return q

def move(p, U):
    q = []
    for i in range(len(p)):
        s = pExact * p[(i-U) % len(p)]
        s = s + pOvershoot * p[(i-U-1) % len(p)]
        s = s + pUndershoot * p[(i-U+1) % len(p)]
        q.append(s)
    return q
#
# ADD CODE HERE
p = sense(p,"red")
p = move(p,1)
p = sense(p,"green")
p = move(p,1)
#
print p # TRUE

# Modify the previous code so that the robot senses red twice.

p = [0.2, 0.2, 0.2, 0.2, 0.2]
world = ['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'green']
motions = [1, 1]
pHit = 0.6
pMiss = 0.2
pExact = 0.8
pOvershoot = 0.1
pUndershoot = 0.1

def sense(p, Z):
    q = []
    for i in range(len(p)):
        hit = (Z == world[i])
        q.append(p[i] * (hit * pHit + (1 - hit) * pMiss))
    s = sum(q)
    for i in range(len(q)):
        q[i] = q[i] / s
    return q

def move(p, U):
    q = []
    for i in range(len(p)):
        s = pExact * p[(i - U) % len(p)]
        s = s + pOvershoot * p[(i - U - 1) % len(p)]
        s = s + pUndershoot * p[(i - U + 1) % len(p)]
        q.append(s)
    return q

for k in range(len(measurements)):
    p = sense(p, measurements[0])
    p = move(p, motions[k])

print p  # TRUE