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 eg1():
# Example to demonstrate interaction detection
# Environment parameters
sidelen = 100.
# Measurement parameters
sig = 5.
g = 6
t = 60.
obstimes1 = [0.,20.,40.,t]
obstimes2 = [0.,20.,40.,t]
# Generate graph
G = roadnet.makegridgraph(g,sidelen)
# Vehicle parameters
# Object 1
p1 = [0,1,2,8,9,15,16,22] # path
nseg1 = len(p1)-1
# Start and end point
s01 = 24.
se1 = 36.
# Object 2
p2 = [27,21,15,9,8,7,6,12] # path
# Start and end point
s02 = 55.
se2 = 30.
nseg2 = len(p2)-1
# Statistics for path generation
vmax = 50/3.6
alph = 5.
bet = 1.25
# Meeting parameters
segn = [4,4] # Meeting segment for objects
dres = 50. # Distance along meeting segment for object 1
xM = roadnet.getpos(G,p1,(segn[0]-1)*sidelen+dres,sidelen)
tM = 28.
T = 10.
for j in range(len(obstimes1)):
if obstimes1[j]>(T+tM):
obstimes1[j] += T
for j in range(len(obstimes2)):
if obstimes2[j]>(T+tM):
obstimes2[j] += T
p1bm = p1[0:segn[0]+1]
p1am = p1[(segn[0]-1):(nseg1+1)]
p2bm = p2[0:segn[1]+1]
p2am = p2[(segn[1]-1):(nseg2+1)]
# Algorithm parameters
n = 200 # Sample size for path posterior
n2 = 200 # sample size for position probability approximation
K = 100 # Number of candidate paths
# Movement statistics
vmean = 36/3.6
vvar = 2.*2.
# Generate data
z1 = roadnet.makedata2(G,p1bm,p1am,xM,tM,T,obstimes1,s01,se1,sig,vmax,alph,bet)
z2 = roadnet.makedata2(G,p2bm,p2am,xM,tM,T,obstimes2,s02,se2,sig,vmax,alph,bet)
plt.figure(1)
plt.clf()
roadnet.plotpath(G,[p1,p2],'-',0.)
plt.plot(xM[0],xM[1],'s',markerfacecolor='orange',markeredgecolor='orange',markersize=9.,markeredgewidth=3.)
plt.xlabel('x-position (m)',fontsize=16)
plt.ylabel('y-position (m)',fontsize=16)
plt.tick_params(axis='both', which='major', labelsize=14)
# Times at which interaction is considered
ntpts = 51
tax = numpy.linspace(10,60,ntpts)
t0 = time.time()
[H,P1,P2,s1,eidx1] = calcinter(G,z1,obstimes1,z2,obstimes2,n,n2,K,tax,1000,vmean,vvar,sig*sig)
et = time.time()-t0
# Plot results
plt.figure(2)
plt.clf()
roadnet.plotpath(G,[p1,p2],'-',0.)
for j in range(len(z1)):
plt.plot(z1[j][0],z1[j][1],'bo',mew=0.,ms=8.)
for j in range(len(z2)):
plt.plot(z2[j][0],z2[j][1],'ro',mew=0.,ms=8.)
plt.figure(3)
plt.clf()
Hdiag = numpy.diag(H)
plt.plot(tax,Hdiag,linewidth=2.5)
plt.xlabel('t (s)',fontsize=16)
plt.ylabel('H(t,t)',fontsize=16)
plt.tick_params(axis='both', which='major', labelsize=14)
plt.axis([tax[0],tax[-1],0,1])
plt.grid(True)
# Meeting place
idxmax = numpy.argmax(Hdiag)
plt.figure(2)
plot_samp_pos(G,s1[idxmax],eidx1[idxmax])
plt.plot(xM[0],xM[1],'s',markerfacecolor='orange',markeredgecolor='orange',markersize=9.,markeredgewidth=3.)
plt.xlabel('x-position (m)',fontsize=16)
plt.ylabel('y-position (m)',fontsize=16)
plt.tick_params(axis='both', which='major', labelsize=14)
fig = plt.figure(4)
plt.clf()
[tx,ty] = numpy.meshgrid(tax,tax)
ax = fig.gca(projection='3d')
ax.plot_surface(tx,ty,H,rstride=1,cstride=1,cmap=cm.jet)
ax.set_xlabel('t1 (s)',fontsize=16)
ax.set_ylabel('t2 (s)',fontsize=16)
ax.set_zlabel('H(t1,t2)',fontsize=16)
ax.set_zlim3d(0,1)
for label in ax.get_xticklabels() + ax.get_yticklabels() + ax.get_zticklabels():
label.set_fontsize(14)
# plt.show()
return H,tax
def sim1(g,nsim,t,m,n):
# [rmse,rhist] = sim1(g,nsim,t,m,n):
# Simulation for performance assessment using random paths
# Inputs:
# g- size of grid network
# nsim- number of simuations
# t- surveillance duration
# m- number of equispaced (in time) position measurements
# n- sample size for algorithm
# Outputs:
# rmse: RMS error between the true path and the MAP path (spatial)
# rhist: histogram of rank of true path
# Environment parameters
sidelen = 100
# Measurement parameters
sig = 5. # measurement standard deviation
s0 = 30. # starting location along first edge
obstimes = [0 for j in range(m)]
for j in range(m):
obstimes[j] = j*t/(m-1)
# Vehicle parameters
vmax = 50./3.6
a = 5.
b = 1.25
vmean = vmax*a/(a+b)
# Algorithm parameters
K = 100 # minimum number of candidate paths
vmean = 10. # mean velocity
vvar = 4. # velocity variance
# Generate graph
G = roadnet.makegridgraph(g,sidelen)
rmse = [0. for j in range(len(n))]
rhist = [[0 for i in range(n[j])] for j in range(len(n))]
for i in range(nsim):
# Generate random path and data
[p,se,z] = mystats.gen_rand_path(G,t,s0,vmax,a,b,obstimes,sig)
for j in range(len(n)):
print i, j
t0 = time.time()
[pp,sep,wp] = calcpostprobs(G,z,obstimes,n[j],K,vmean,vvar,sig*sig)
et = time.time()-t0
# Generate output statistics
np = len(pp)
idxsort = numpy.argsort(wp)
idxmax = numpy.argmax(wp)
rmse_samp = [0 for k in range(np)]
for k, psamp in enumerate(pp):
rmse_samp[k] = mystats.calc_path_rmse(G,s0,p,se,psamp,sep[k])
idxminrmse = numpy.argmin(rmse_samp)
rhist[j][idxsort[idxminrmse]] += 1./nsim
rmse[j] = rmse[j]+rmse_samp[idxmax]/nsim
return rmse, rhist
def sim2(nsim):
# Environment parameters
sidelen = 100.0
# Measurement parameters
sig = 5.0
g = 5
t = 45.0
obstimes1_w = [10.0, 16.0, 30.0, 40.0] # [10,15,20] # way points only at this point
obstimes2_w = [6.0, 13.0, 27.0, 36.0]
# Generate graph
G = roadnet.makegridgraph(g, sidelen)
# Vehicle parameters
p1 = [0, 1, 6, 7, 12, 11, 16]
nseg1 = len(p1) - 1
p2 = [13, 12, 7, 6, 1, 2, 3]
nseg2 = len(p2) - 1
vmax = 60 / 3.6
alph = 5.0
bet = 1.25
# Meeting parameters
segn = [3, 3] # Meeting segment for objects
dres = 50.0 # Distance along meeting segment for object 1
xM = roadnet.getpos(G, p1, (segn[0] - 1) * sidelen + dres, sidelen)
tM = 21.0
T = 0.0
t = t + T
p1bm = p1[0 : segn[0] + 1]
p1am = p1[(segn[0] - 1) : (nseg1 + 1)]
p2bm = p2[0 : segn[1] + 1]
p2am = p2[(segn[1] - 1) : (nseg2 + 1)]
print p2bm
print p1bm
print p2am
print p1am
print xM
# Algorithm parameters
n = 400
K = 10
m1 = 2
m2 = 2
# 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
random.seed(2.0)
z1 = roadnet.makedata2(G, p1bm, p1am, xM, tM, T, t, obstimes1_w, sig, vmax, alph, bet)
z2 = roadnet.makedata2(G, p2bm, p2am, xM, tM, T, t, obstimes2_w, sig, vmax, alph, bet)
random.seed()
roadnet.plotpath(G, p2)
xpos = z2[0, :]
ypos = z2[1, :]
plt.plot(xpos, ypos, "rx")
print z1
print z2
ntpts = 7
tax = numpy.linspace(16, 22, ntpts)
bcoeff = numpy.zeros((nsim, ntpts))
tmax = numpy.zeros((nsim))
for cnt in range((nsim)):
print cnt
# Generate data
# z1 = roadnet.makedata2(G,p1bm,p1am,xM,tM,T,t,obstimes1_w,sig,vmax,alph,bet)
# z2 = roadnet.makedata2(G,p2bm,p2am,xM,tM,T,t,obstimes2_w,sig,vmax,alph,bet)
# First stage of processing (case 1 for each object)
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)):
idx = k + i * n
if isvalid1[idx]:
# print candp[i]
for j in range(len(obstimes1)):
pos = roadnet.getpos(G, candp1[i], datamat1[idx, j], sidelen)
xpts1[idx, 2 * j] = pos[0]
xpts1[idx, 2 * j + 1] = pos[1]
print isvalid2.sum()
xpts2 = numpy.zeros((n * numcandp2, 2 * len(obstimes2)))
for i in range((numcandp2)):
for k in range((n)):
idx = k + i * n
if isvalid2[idx]:
# print candp[i]
for j in range(len(obstimes2)):
pos = roadnet.getpos(G, candp2[i], datamat2[idx, j], sidelen)
if i == 14:
plt.plot(pos[0], pos[1], "g.")
xpts2[idx, 2 * j] = pos[0]
xpts2[idx, 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
print 1 / sum(ww1 ** 2)
print 1 / sum(ww2 ** 2)
w1cdf = numpy.cumsum(ww1)
w2cdf = numpy.cumsum(ww2)
maxval = -1.0
for a in range((ntpts)):
# print a
random.seed(3.0)
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 pos
# MC approximation of p1 and p2
random.seed(4.0)
uk = random.uniform(0, 1.0 / m2)
l1 = 0
l2 = 0
post1 = 0.0
post2 = 0.0
# 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)
print pos1
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]
# print tcum1[l1,:]
# print tleft
# print vmax*tleft
# print res2
print (sidelen - res2)
print tleft
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 post1, post2
if post2 > 1e-20:
bcoeff[cnt, a] = bcoeff[cnt, a] + math.sqrt(post1 / post2) / m1
uj = uj + 1.0 / m1
if bcoeff[cnt, a] > maxval:
maxval = bcoeff[cnt, a]
tmax[cnt] = tax[a]
# print bcoeff
return bcoeff, tmax
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