def eg1():
# Set up for demonstration of case 1 algorithm
# This returns the path posterior probabilities for the given example
# Environment parameters
sidelen = 100
# Measurement parameters
sig = 0.5 # measurement standard deviation
g = 5 # network grid size
t = 45. # surveillance duration
s0 = 20. # starting location along first edge
se = 45. # ending location along final edge
obstimes = [0.,22.,t] # observation times
# Vehicle parameters
p = [0,1,2,7,12,17,18] # path nodes
# Parameters used for path generation
vmax = 60./3.6
a = 5.
b = 1.25
# Algorithm parameters
n = 100 # number of samples
K = 100 # minimum number of candidate paths
vmean = 10. # mean velocity
vvar = 4. # velocity variance
# Generate graph
G = roadnet.makegridgraph(g,sidelen)
# Generate data
tact = 0
while abs(tact-t)>0.01:
[z,tact] = roadnet.makedata(G,p,obstimes,s0,se,sig,vmax,a,b)
t0 = time.time()
[pp,sep,wp] = calcpostprobs(G,z,obstimes,n,K,vmean,vvar,sig*sig)
et = time.time()-t0
print et
# Plot best paths
np = len(pp)
idxsort = numpy.argsort(wp)
nplot = min([3,np])
plt.figure(1)
roadnet.plotpath(G,[p,pp[idxsort[np-1]],pp[idxsort[np-2]]],'-',0.)
for j in range(len(z)):
plt.plot(z[j][0],z[j][1],'kx',markersize=10.,markeredgewidth=2)
plt.show()
return pp, wp
def sim1(nsim):
# Environment parameters
sidelen = 100.0
# Measurement parameters
sig = 5.0
g = 5
t = 60
t = 40.0
obstimes1_w = [10] # [10,15,20] # way points only at this point
obstimes2_w = [5, 20]
# Vehicle parameters
# p = [0,1,7,13,14,15,21,22]
p1 = [0, 1, 6, 7, 12, 11, 16]
p2 = [13, 12, 7, 6, 1, 2]
# p = [0,1,2,7]
vmax = 60 / 3.6
alph = 5
bet = 1.25
# Algorithm parameters
n = 100
K = 5
m1 = 10
m2 = 10
# Generate graph
G = roadnet.makegridgraph(g, sidelen)
# Generate candidate paths
numcandp1 = 0
d1 = 0
while numcandp1 < K:
candp1 = list(nx.all_simple_paths(G, p1[0], p1[-1], d1))
numcandp1 = len(candp1)
d1 = d1 + 1
numcandp2 = 0
d2 = 0
while numcandp2 < K:
candp2 = list(nx.all_simple_paths(G, p2[0], p2[-1], d2))
numcandp2 = len(candp2)
d2 = d2 + 1
# print numcandp
# Put in a suitable format for processing
segls1 = numpy.zeros((numcandp1, d1 - 1))
for i in range(numcandp1):
print candp1[i]
for j in range(len(candp1[i]) - 1):
segls1[i, j] = sidelen
segls2 = numpy.zeros((numcandp2, d2 - 1))
for i in range(numcandp2):
print candp2[i]
for j in range(len(candp2[i]) - 1):
segls2[i, j] = sidelen
# Generate data
tact = 0
while abs(tact - t) > 0.01:
[z1, tact] = roadnet.makedata(G, p1, obstimes1_w, sig, vmax, alph, bet)
tact = 0
while abs(tact - t) > 0.01:
[z2, tact] = roadnet.makedata(G, p2, obstimes2_w, sig, vmax, alph, bet)
for cnt in range((nsim)):
print cnt
# Generate data
tact = 0
while abs(tact - t) > 0.01:
[z1, tact] = roadnet.makedata(G, p1, obstimes1_w, sig, vmax, alph, bet)
tact = 0
while abs(tact - t) > 0.01:
[z2, tact] = roadnet.makedata(G, p2, obstimes2_w, sig, vmax, alph, bet)
# First stage of processing
obstimes1 = numpy.zeros((len(obstimes1_w) + 2))
obstimes1[0] = 0.0
for i in range(len(obstimes1_w)):
obstimes1[i + 1] = obstimes1_w[i]
obstimes1[-1] = t
obstimes2 = numpy.zeros((len(obstimes2_w) + 2))
obstimes2[0] = 0.0
for i in range(len(obstimes2_w)):
obstimes2[i + 1] = obstimes2_w[i]
obstimes2[-1] = t
[datamat1, isvalid1, pP01, v1, tcum1] = case2.arclgen(obstimes1, segls1, n, vmax, alph, bet)
[datamat2, isvalid2, pP02, v2, tcum2] = case2.arclgen(obstimes2, segls2, n, vmax, alph, bet)
# Convert to positions in 2D space
xpts1 = numpy.zeros((n * numcandp1, 2 * len(obstimes1)))
for i in range((numcandp1)):
for k in range((n)):
cnt = k + i * n
if isvalid1[cnt]:
# print candp[i]
for j in range(len(obstimes1)):
pos = roadnet.getpos(G, candp1[i], datamat1[cnt, j], sidelen)
xpts1[cnt, 2 * j] = pos[0]
xpts1[cnt, 2 * j + 1] = pos[1]
xpts2 = numpy.zeros((n * numcandp2, 2 * len(obstimes2)))
for i in range((numcandp2)):
for k in range((n)):
cnt = k + i * n
if isvalid2[cnt]:
# print candp[i]
for j in range(len(obstimes2)):
pos = roadnet.getpos(G, candp2[i], datamat2[cnt, j], sidelen)
xpts2[cnt, 2 * j] = pos[0]
xpts2[cnt, 2 * j + 1] = pos[1]
# print datamat[cnt,:]
# print xpts[cnt,:]
[pP1, w1, pP1w, ww1] = case2.calcpostprobs(z1, xpts1, isvalid1, pP01, sig)
[pP2, w2, pP2w, ww2] = case2.calcpostprobs(z2, xpts2, isvalid2, pP02, sig)
print pP1w
print pP2w
npts = 20
tax = numpy.linspace(1, 35, npts)
bcoeff = numpy.zeros(npts)
w1cdf = numpy.cumsum(ww1)
w2cdf = numpy.cumsum(ww2)
for a in range((npts)):
# print a
uj = random.uniform(0, 1.0 / m1)
i = 0
for j in range((m1)):
while w2cdf[i] < uj:
i = i + 1
# Find s
pathidx = i / n
[snum, seg, pos] = roadnet.getseg(G, candp2[pathidx], v2[i, :], tcum2[i, :], tax[a], sidelen)
res2 = abs((pos - G.node[candp2[pathidx][snum]]["pos"]).sum())
# print seg
# MC approximation of p1 and p2
uk = random.uniform(0, 1.0 / m2)
l1 = 0
l2 = 0
post1 = 0
post2 = 0
# print i, ww2[i]
for k in range((m2)):
while w1cdf[l1] < uk:
l1 = l1 + 1
while w2cdf[l2] < uk:
l2 = l2 + 1
pathidx1 = l1 / n
[snum1, seg1, pos1] = roadnet.getseg(G, candp1[pathidx1], v1[l1, :], tcum1[l1, :], tax[a], sidelen)
if (seg1[0] == seg[0]) and (seg1[1] == seg[1]):
if snum1 > 0:
tleft = tax[a] - tcum1[l1, snum1 - 1]
else:
tleft = tax[a]
post1 = post1 + scipy.stats.beta.pdf(res2 / (vmax * tleft), alph, bet) / (m2 * vmax * tleft)
elif (seg1[0] == seg[1]) and (seg1[1] == seg[0]):
if snum1 > 0:
tleft = tax[a] - tcum1[l1, snum1 - 1]
else:
tleft = tax[a]
post1 = post1 + scipy.stats.beta.pdf((sidelen - res2) / (vmax * tleft), alph, bet) / (
m2 * vmax * tleft
)
pathidx2 = l2 / n
[snum2, seg2, pos2] = roadnet.getseg(G, candp2[pathidx2], v2[l2, :], tcum2[l2, :], tax[a], sidelen)
# print seg, seg2
if (seg2[0] == seg[0]) and (seg2[1] == seg[1]):
if snum2 > 0:
tleft = tax[a] - tcum2[l2, snum2 - 1]
else:
tleft = tax[a]
post2 = post2 + scipy.stats.beta.pdf(res2 / (vmax * tleft), alph, bet) / (m2 * vmax * tleft)
uk = uk + 1.0 / m2
# print p1, p2
if post2 > 1e-20:
bcoeff[a] = bcoeff[a] + math.sqrt(post1 / post2) / m1
uj = uj + 1.0 / m1
print bcoeff
return ww1, ww2
