In [1]:
import numpy as np
from matplotlib import pyplot as plt
import random
from math import sqrt, pi, exp
from sklearn.naive_bayes import GaussianNB
import math
from collections import Counter
In [2]:
def gaussian_prob(obs, mu, sig):
num = (obs - mu)**2
denum = 2*sig**2
norm = 1 / sqrt(2*pi*sig**2)
return norm * exp(-num/denum)
class GNB():
def __init__(self, priors):
self.priors = priors
self.classes = range(len(priors))
self.trained = False
def train(self, X, Y):
num_vars = len(X[0])
self.num_vars = num_vars
totals_by_label = [[[] for i in range(num_vars)] for j in self.classes]
label_counts = Counter()
for x, lab in zip(X,Y):
label_counts[lab] += 1
for i,val in enumerate(x):
totals_by_label[lab][i].append(val)
print totals_by_label
means = []
stds = []
for i in self.classes:
means.append([])
stds.append([])
for arr in totals_by_label[i]:
mean = np.mean(arr)
std = np.std(arr)
means[-1].append(mean)
stds[-1].append(std)
self._means = means
self._stds = stds
self.trained = True
def _predict(self, obs):
if not self.trained:
print "Can't Predict before training!"
return
assert len(obs) == self.num_vars
probs = []
for (means, stds, lab) in zip(self._means, self._stds, self.classes):
print 'product is 1'
product = 1
for mu, sig, o in zip(means, stds, obs):
likelihood = gaussian_prob(o, mu, sig)
product *= likelihood
probs.append(product)
t = sum(probs)
return [p/t for p in probs]
LANE_WIDTH = 4
NUM_LANES = 3
DT = 0.2
class Predictor(object):
transition_prob = 0.05
new_data_weight = 0.5
def __init__(self):
self.vehicles = {}
self.gnb = GNB([1.0 / 3 for i in range(3)])
def update(self, observations):
"""
observations - json array, where each entry is
1 vehicle which looks like like:
{
"id": 201,
"s" : 104.2,
"d" : 6.1,
"s_dot" : 12.0,
"d_dot" : -1.2,
"lane" : 1
}
"""
all_beliefs = {}
for vehicle in observations:
_id = vehicle['id']
# add vehicle w/ prior probs
if _id not in self.vehicles:
lane = vehicle['lane']
beliefs = [0.0 for _ in range(NUM_LANES)]
beliefs[lane] = 1.0
neighbors = [lane-1,lane+1]
if neighbors[0] < 0: neighbors.pop(0)
if neighbors[-1] >= NUM_LANES: neighbors.pop()
assert len(neighbors) >= 1
for n in neighbors:
beliefs[lane] = beliefs[lane] - Predictor.transition_prob
beliefs[n] += Predictor.transition_prob
vehicle['beliefs'] = beliefs
self.vehicles[_id] = vehicle
# update probabilities
s = vehicle['s']
d = vehicle['d']
s_dot = vehicle['s_dot']
d_dot = vehicls['d_dot']
obs = [s,d,s_dot,d_dot]
likelihoods = self.gnb._predict(obs)
new_beliefs = []
for prev, new in zip(self.vehicles[_id]['beliefs'], likelihoods):
new_bel = prev + Predictor.new_data_weight*new
new_beliefs.append(new_bel)
T = sum(new_beliefs)
final = [b/T for b in new_beliefs]
self.vehicles[_id]['beliefs'] = final
all_beliefs[_id] = final
return all_beliefs
In [5]:
LANE_WIDTH = 4
ROAD_LENGTH = 100
SPEED = 10
NUM_LANES = 3
def generate_labeled_data(N):
trajectories = []
labels = []
for i in range(N):
start_lane = random.choice([0,1,2])
label = "keep"
if start_lane == 0:
end_lane = random.choice([0,1])
elif start_lane == 1:
end_lane = random.choice([0,1,2])
else:
end_lane = random.choice([1,2])
if end_lane > start_lane:
label = "right"
elif end_lane < start_lane:
label = "left"
start_s = 0.0
dist = random.gauss(40, 3)
end_s = start_s + dist
start_d = LANE_WIDTH * start_lane + random.gauss(0, float(LANE_WIDTH) / 10)
end_d = LANE_WIDTH * end_lane + random.gauss(0, float(LANE_WIDTH) / 10)
speed = max(random.gauss(SPEED, 1.0), 6)
T = (end_s - start_s) / speed
alpha_s = JMT([start_s, speed, 0], [end_s, speed + random.gauss(0,0.5), 0], T)
alpha_d = JMT([start_d, 0, 0], [end_d, 0, 0], T)
s = to_equation(alpha_s)
s_dot = to_equation(differentiate(alpha_s))
d = to_equation(alpha_d)
d_dot = to_equation(differentiate(alpha_d))
coords = []
for i in range(0, int(T*100), int(T) ):
t = float(i) / 100
coords.append((s(t), d(t), s_dot(t), d_dot(t)))
trajectories.append(coords)
labels.append(label)
return trajectories, labels
def differentiate(coefficients):
new_cos = []
for deg, prev_co in enumerate(coefficients[1:]):
new_cos.append((deg+1) * prev_co)
return new_cos
N = 1000
trajs, labels = generate_labeled_data(N)
TRAIN_DATA = trajs[:3 * N / 4]
TRAIN_LABELS = labels[:3 * N / 4]
TEST_DATA = trajs[3 * N / 4:]
TEST_LABEL = labels[3 * N / 4:]
T = 15
def process_obs(obs):
s,d,s_dot, d_dot = obs
return (
s,
# (d % LANE_WIDTH) ** 2,
# d_dot ** 2,
# abs(d),
# d/d_dot,
)
def train_naive_bayes(data,labels, t):
X = []
transform_label = {'left' : -1, 'keep' : 0, 'right' : 1}
Y = [transform_label[lab] for lab in labels]
for trajectory in data:
obs = trajectory[t]
X.append(process_obs(obs))
clf = GaussianNB()
clf.fit(X, Y)
return clf
clf = train_naive_bayes(TRAIN_DATA, TRAIN_LABELS, T)
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[ 0.04413139 -0.01353157 0.00011061]
[-0.45023909 0.10310008 -0.00057231]
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[-0.28895513 0.06240117 -0.0002914 ]
[ -1.98772866e-03 5.83166700e-04 -4.19580771e-06]
[-0.41243737 0.09039609 -0.00044099]
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[ -6.16922373e-03 8.91208468e-04 -1.26157963e-06]
[ 3.65322705e-02 -1.08234642e-02 8.01140761e-05]
[ -2.68381621e-02 5.93974727e-03 -2.98199732e-05]
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[ 3.12106244e-02 -6.88896390e-03 2.15843379e-05]
[ 3.14804023e-04 -5.19933395e-05 1.09655731e-07]
[-0.10493329 0.0274676 -0.00014185]
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[ -4.83978170e-02 1.21987946e-02 -5.64113720e-05]
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[ 1.98871384e-03 -3.31934199e-04 7.22322278e-07]
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[ -1.58662278e-01 2.79200913e-02 -7.10940088e-05]
[ -2.86671440e-02 8.58289755e-03 -6.54895991e-05]
[-0.34230851 0.07655254 -0.00039632]
[ 2.45563300e-02 -6.92420916e-03 4.44029889e-05]
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[ -2.78285239e-02 4.80828969e-03 -1.15961313e-05]
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[-0.46564159 0.10411949 -0.00053882]
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[-0.43439012 0.09614055 -0.0004827 ]
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[ 3.16740358e-02 -7.41575807e-03 2.76284043e-05]
[ -9.62507749e-03 1.68575310e-03 -4.23264043e-06]
[ -8.67479883e-03 1.79382546e-03 -4.63793192e-06]
[ -1.46253766e-01 2.26360760e-02 -3.93492204e-05]
[ -6.56543645e-04 1.51621660e-04 -5.42605084e-07]
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[ 2.48737343e-02 -5.24993686e-03 2.29119326e-05]
[ 6.44196639e-03 -1.72132784e-03 9.43906598e-06]
[ -2.71224990e-01 5.41749576e-02 -2.00855858e-04]
[ 8.26464110e-03 -1.70498279e-03 4.37766267e-06]
[ 1.18600372e-02 -1.83129942e-03 3.16122399e-06]
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[ -2.97204079e-02 5.53713460e-03 -1.67019989e-05]
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[ -7.92935677e-02 1.93890842e-02 -8.20473130e-05]
[ 2.05024845e-01 -3.74945353e-02 1.07032166e-04]
[ 2.27639348e-02 -5.72141527e-03 2.62386763e-05]
[ -2.76218222e-01 5.19142309e-02 -1.60712729e-04]
[ -1.85673464e-02 5.30437371e-03 -3.53314501e-05]
[ -3.31092672e-01 7.06757175e-02 -3.18916993e-04]
[ 3.77756696e-03 -1.26642643e-03 1.33834935e-05]
[ 2.33767006e-02 -5.84857910e-03 4.21198427e-05]
In [4]:
def JMT(start, end, T):
a_0, a_1, a_2 = start[0], start[1], start[2] / 2.0
c_0 = a_0 + a_1 * T + a_2 * T**2
c_1 = a_1 + a_2 * T
c_2 = 2 * a_2
A = np.array([
[ T**3, T**4, T**5],
[3*T**2, 4*T**3, 5*T**4],
[6*T, 12*T**2, 20*T**5],
])
B = np.array([
end[0] - c_0,
end[1] - c_1,
end[2] - c_2
])
a_3_4_5 = np.linalg.solve(A,B)
print a_3_4_5
alphas = np.concatenate([np.array([a_0, a_1, a_2]), a_3_4_5])
return alphas
def to_equation(coefficients):
def f(t):
total = 0.0
for i, c in enumerate(coefficients):
total += c * t ** i
return total
return f
def PTG(start_s, start_d, end_s, end_d, T, time_step = 0.1):
s_coefficients = JMT(start_s, end_s, T)
d_coefficients = JMT(start_d, end_d, T)
print "s_coefficients: {}".format(s_coefficients)
s = to_equation(s_coefficients)
d = to_equation(d_coefficients)
coords = []
t = 0
while t <= T:
new = (s(t), d(t), t)
coords.append(new)
t += time_step
return coords
In [95]:
gnb = GNB([0.5, 0.5])
In [96]:
X = [
[3, 4, 5],
[5, 6, 7],
[-3,-2,-1],
[-4,-1,0]
]
Y = [0, 0, 1, 1]
In [97]:
gnb.train(X,Y)
[[[3, 5], [4, 6], [5, 7]], [[-3, -4], [-2, -1], [-1, 0]]]
In [98]:
gnb._means
Out[98]:
[[4.0, 5.0, 6.0], [-3.5, -1.5, -0.5]]
In [99]:
gnb.classes
Out[99]:
[0, 1]
In [92]:
gnb._stds
Out[92]:
[[1.0, 1.0, 1.0], [0.5, 0.5, 0.5]]
In [107]:
gnb._predict([1.0, -1, 0])
product is 1
product is 1
Out[107]:
[0.2536117142620282, 0.7463882857379717]
In [ ]:
def write_to_file(data, labels, fname):
with open(fname, 'wb') as f:
for label, coords in zip(labels, data):
s = "{} "
Content source: mlandry1/CarND
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