1 # The function localize takes the following arguments:  2 #  3 # colors:  4 #        2D list, each entry either ‘R‘ (for red cell) or ‘G‘ (for green cell)  5 #  6 # measurements:  7 #        list of measurements taken by the robot, each entry either ‘R‘ or ‘G‘  8 #  9 # motions: 10 #        list of actions taken by the robot, each entry of the form [dy,dx], 11 #        where dx refers to the change in the x-direction (positive meaning 12 #        movement to the right) and dy refers to the change in the y-direction 13 #        (positive meaning movement downward) 14 #        NOTE: the *first* coordinate is change in y; the *second* coordinate is 15 #              change in x 16 # 17 # sensor_right: 18 #        float between 0 and 1, giving the probability that any given 19 #        measurement is correct; the probability that the measurement is 20 #        incorrect is 1-sensor_right 21 # 22 # p_move: 23 #        float between 0 and 1, giving the probability that any given movement 24 #        command takes place; the probability that the movement command fails 25 #        (and the robot remains still) is 1-p_move; the robot will NOT overshoot 26 #        its destination in this exercise 27 # 28 # The function should RETURN (not just show or print) a 2D list (of the same 29 # dimensions as colors) that gives the probabilities that the robot occupies 30 # each cell in the world. 31 # 32 # Compute the probabilities by assuming the robot initially has a uniform 33 # probability of being in any cell. 34 # 35 # Also assume that at each step, the robot: 36 # 1) first makes a movement, 37 # 2) then takes a measurement. 38 # 39 # Motion: 40 #  [0,0] - stay 41 #  [0,1] - right 42 #  [0,-1] - left 43 #  [1,0] - down 44 #  [-1,0] - up 45 def sense(p,colors,measurement,sensor_right): 46     q=[] 47     for row in range(len(colors)): 48         temp=[] 49         for col in range(len(colors[0])): 50             hit = (measurement == colors[row][col]) 51             temp.append(p[row][col] * (hit * sensor_right + (1-hit) * (1-sensor_right))) 52         q.append(temp) 53     s=0 54     for row in range(len(q)): 55         for col in range(len(q[0])): 56             s += q[row][col] 57     for row in range(len(p)): 58         for col in range(len(q[0])): 59             q[row][col] = q[row][col]/s 60     return q 61  62 def move(p, motion, p_move): 63     q = [] 64     for row in range(len(colors)): 65         temp=[] 66         for col in range(len(colors[0])): 67             s = p_move * p[(row - motion[0]) % len(colors)][(col - motion[1]) % len(colors[0])] 68             s += (1-p_move) * p[row][col] 69             temp.append(s) 70         q.append(temp) 71     return q 72          73 def localize(colors,measurements,motions,sensor_right,p_move): 74     # initializes p to a uniform distribution over a grid of the same dimensions as colors 75     pinit = 1.0 / float(len(colors)) / float(len(colors[0])) 76     p = [[pinit for row in range(len(colors[0]))] for col in range(len(colors))] 77      78     # >>> Insert your code here <<< 79      80     for k in range(len(motions)): 81         p = move(p, motions[k],p_move) 82         p = sense(p,colors,measurements[k],sensor_right) 83      84     return p 85  86 def show(p): 87     rows = [‘[‘ + ‘,‘.join(map(lambda x: ‘{0:.5f}‘.format(x),r)) + ‘]‘ for r in p] 88     print ‘[‘ + ‘,\n ‘.join(rows) + ‘]‘ 89      90 ############################################################# 91 # For the following test case, your output should be  92 # [[0.01105, 0.02464, 0.06799, 0.04472, 0.02465], 93 #  [0.00715, 0.01017, 0.08696, 0.07988, 0.00935], 94 #  [0.00739, 0.00894, 0.11272, 0.35350, 0.04065], 95 #  [0.00910, 0.00715, 0.01434, 0.04313, 0.03642]] 96 # (within a tolerance of +/- 0.001 for each entry) 97  98 colors = [[‘R‘,‘G‘,‘G‘,‘R‘,‘R‘], 99           [‘R‘,‘R‘,‘G‘,‘R‘,‘R‘],100           [‘R‘,‘R‘,‘G‘,‘G‘,‘R‘],101           [‘R‘,‘R‘,‘R‘,‘R‘,‘R‘]]102 measurements = [‘G‘,‘G‘,‘G‘,‘G‘,‘G‘]103 motions = [[0,0],[0,1],[1,0],[1,0],[0,1]]104 p = localize(colors,measurements,motions,sensor_right = 0.7, p_move = 0.8)105 show(p) # displays your answer