def main():
P0 = np.array([[2.0,0.0],[0.0,1.0]])
Ns = 100
Ts = 4.0
(tsim,XK,YK,mu0,dt,tf) = generate_data.execute_sim(cp_dynamics.eqom_stoch_cluster,Ts,30*Ts,Ns,P0,cluster=True,informative=True)
Qk = np.array([[0.005]])
Rk = np.array([[0.01]])
# number of steps in each simulation
nSteps = len(tsim)
nees_history = np.zeros((nSteps,Ns))
e_sims = np.zeros((Ns*nSteps,2))
count_good = 0
count_singular_covariance = 0
count_large_errors = 0
for counter in range(Ns):
xk = XK[:,(2*counter):(2*counter+2)]
yk = YK[:,counter]
(xf,Pf,simOut) = ekf_test(dt,tf,mu0,P0,yk,Qk,Rk)
if simOut.singular_covariance:
print("Simulation exited with singular covariance at index %d" % (simOut.last_index))
count_singular_covariance = count_singular_covariance + 1
continue
# compute the unit variance transformation of the error
e1 = np.zeros((nSteps,2))
chi2 = np.zeros(nSteps)
(e1[0:simOut.last_index,:],chi2[0:simOut.last_index]) = trials_processing.computeErrors(xf[0:simOut.last_index,:],Pf[0:simOut.last_index,:,:],xk[0:simOut.last_index,:])
nees_history[:,counter] = chi2.copy()
mean_nees = np.sum(chi2)/float(nSteps)
print(mean_nees)
# mean NEES
mse = np.sum(np.power(e1,2.0),axis=0)/float(nSteps)
e_sims[(counter*nSteps):(counter*nSteps+nSteps),:] = e1.copy()
if (mse[0] > 1.0) or (mse[1] > 1.0):
count_large_errors = count_large_errors + 1
continue
count_good = count_good + 1
print("MSE: %f,%f" % (mse[0],mse[1]))
# chi-square test statistics
# (alpha) probability of being less than the returned value: stats.chi2.ppf(alpha,df=Nsims)
if Ns < 2:
trials_processing.printSingleSim(tsim,xf,Pf,xk,name='ekf',save_flag=None,history_lines=True,draw_snapshots=False)
#trials_processing.errorParsing(e_sims,nees_history,'ekf','sims_01_bifurcation')
# write to file
# Ns, count_good, count_singular_covariance, count_large_errors, Qk[0,0], Ts
fname = 'ekf_data.txt'
FID = open(fname,'a')
FID.write("%d,%d,%d,%d,%g,%g\n" % (Ns,count_good,count_singular_covariance,count_large_errors,Qk[0,0],Ts))
FID.close()
print("Leaving ekf_trials")
return
def main():
P0 = np.array([[2.0,0.0],[0.0,1.0]])
Ns = 100
Ts = 5.0
(tsim,XK,YK,mu0,dt,tf) = generate_data.execute_sim(cp_dynamics.eqom_stoch_cluster,Ts,30*Ts,Ns,P0,cluster=True,informative=True)
# number of particles
Nsu = 200
Qk = np.array([[0.1]])
Rk = np.array([[0.01]])
# number of steps in each simulation
nSteps = len(tsim)
nees_history = np.zeros((nSteps,Ns))
e_sims = np.zeros((Ns*nSteps,2))
count_good = 0
count_singular_covariance = 0
count_large_errors = 0
for counter in range(Ns):
xk = XK[:,(2*counter):(2*counter+2)]
yk = YK[:,counter]
(xf,Pf,px1,px2,weights,simOut) = sir_test(dt,tf,mu0,P0,yk,Qk,Rk,Nsu)
if simOut.singular_covariance:
print("Simulation exited with singular covariance at index %d" % (simOut.last_index))
count_singular_covariance = count_singular_covariance + 1
continue
# errors
e1 = xk-xf
# mean NEES
mse = np.sum(np.power(xk-xf,2.0),axis=0)/float(nSteps)
e_sims[(counter*nSteps):(counter*nSteps+nSteps),:] = xk-xf
print("MSE: %f,%f" % (mse[0],mse[1]))
if (mse[0] > 1.0) or (mse[1] > 1.0):
count_large_errors = count_large_errors + 1
continue
count_good = count_good + 1
if Ns < 2:
trials_processing.printSingleSim(tsim,xf,Pf,xk,name='sir',save_flag=None,history_lines=True,draw_snapshots=False)
fname = 'sir_data.txt'
FID = open(fname,'a')
FID.write("%d,%d,%d,%d,%g,%g\n" % (Ns,count_good,count_singular_covariance,count_large_errors,Qk[0,0],Ts))
FID.close()
raw_input("Return to quit")
print("Leaving sir_trials")
return
def main():
P0 = np.array([[2.0,0.0],[0.0,1.0]])
Ns = 100
Ts = 3.5
(tsim,XK,YK,mu0,dt,tf) = generate_data.execute_sim(cp_dynamics.eqom_stoch_cluster,Ts,30*Ts,Ns,P0,cluster=True,informative=True)
flag_adapt = False
Qk = np.array([[0.01]])
#Qk = np.array([[0.01*Ts*0.1]])
Rk = np.array([[0.01]])
# number of steps in each simulation
nSteps = len(tsim)
nees_history = np.zeros((nSteps,Ns))
Nf_history = np.zeros((nSteps,Ns))
e_sims = np.zeros((Ns*nSteps,2))
count_good = 0
count_singular_covariance = 0
count_large_errors = 0
for counter in range(Ns):
xk = XK[:,(2*counter):(2*counter+2)]
yk = YK[:,counter]
(xf,Pf,Nf,XKO,simOut) = enkf_test(dt,tf,mu0,P0,yk,Qk,Rk,flag_adapt)
if simOut.singular_covariance:
print("Simulation exited with singular covariance at index %d" % (simOut.last_index))
count_singular_covariance = count_singular_covariance + 1
continue
# store the number of particles, relevant if adaptive
Nf_history[:,counter] = Nf.copy()
# errors
e1 = np.zeros((nSteps,2))
chi2 = np.zeros(nSteps)
(e1[0:simOut.last_index,:],chi2[0:simOut.last_index]) = trials_processing.computeErrors(xf[0:simOut.last_index,:],Pf[0:simOut.last_index,:,:],xk[0:simOut.last_index,:])
nees_history[:,counter] = chi2.copy()
mean_nees = np.sum(chi2)/float(nSteps)
print(mean_nees)
# mean NEES
mse = np.sum(np.power(e1,2.0),axis=0)/float(nSteps)
# get the mean number of particles in time
Nf_mean = np.sum(Nf_history,axis=1)/Ns
e_sims[(counter*nSteps):(counter*nSteps+nSteps),:] = e1.copy()
if (mse[0] > 1.0) or (mse[1] > 1.0):
count_large_errors = count_large_errors + 1
continue
count_good = count_good + 1
print("MSE: %f,%f" % (mse[0],mse[1]))
if Ns < 2:
trials_processing.printSingleSim(tsim,xf,Pf,xk,name='enkf',save_flag=None,history_lines=True,draw_snapshots=False)
if flag_adapt:
fig = plt.figure(figsize=(6.0,3.37)) #figsize tuple is width, height
tilt = "AENKF, Ts = %.2f, %d sims, " % (dt, Ns)
ax = fig.add_subplot(111,ylabel='mean particles',title=tilt)
ax.plot(tsim,Nf_mean,'b-')
ax.grid()
fig.show()
raw_input("Return to close")
#trials_processing.errorParsing(e_sims,nees_history,'enkf','sims_01_bifurcation')
# write to file
# Ns, count_good, count_singular_covariance, count_large_errors, Qk[0,0], Ts
if not flag_adapt:
fname = 'enkf_data.txt'
FID = open(fname,'a')
FID.write("%d,%d,%d,%d,%g,%g\n" % (Ns,count_good,count_singular_covariance,count_large_errors,Qk[0,0],Ts))
FID.close()
else:
fname = 'aenkf_data.txt'
FID = open(fname,'a')
FID.write("%d,%d,%d,%d,%g,%g\n" % (Ns,count_good,count_singular_covariance,count_large_errors,Qk[0,0],Ts))
FID.close()
print("Leaving enkf_trials")
return
def main():
P0 = np.array([[2.0,0.0],[0.0,1.0]])
Ns = 100
Ts = 3.5
(tsim,XK,YK,mu0,dt,tf) = generate_data.execute_sim(cp_dynamics.eqom_stoch_cluster,Ts,30*Ts,Ns,P0,cluster=True,informative=True)
Qk = np.array([[0.01]])
Rk = np.array([[0.01]])
# number of steps in each simulation
nSteps = len(tsim)
nees_history = np.zeros((nSteps,Ns))
e_sims = np.zeros((Ns*nSteps,2))
count_good = 0
count_singular_covariance = 0
count_large_errors = 0
for counter in range(Ns):
xk = XK[:,(2*counter):(2*counter+2)]
yk = YK[:,counter]
(xf,Pf,simOut) = ukf_test(dt,tf,mu0,P0,yk,Qk,Rk)
if simOut.singular_covariance:
print("Simulation exited with singular covariance at index %d" % (simOut.last_index))
count_singular_covariance = count_singular_covariance + 1
continue
# compute the unit variance transformation of the error
e1 = np.zeros((nSteps,2))
chi2 = np.zeros(nSteps)
(e1[0:simOut.last_index,:],chi2[0:simOut.last_index]) = trials_processing.computeErrors(xf[0:simOut.last_index,:],Pf[0:simOut.last_index,:,:],xk[0:simOut.last_index,:])
nees_history[:,counter] = chi2.copy()
mean_nees = np.sum(chi2)/float(nSteps)
print(mean_nees)
# mean NEES
mse = np.sum(np.power(e1,2.0),axis=0)/float(nSteps)
e_sims[(counter*nSteps):(counter*nSteps+nSteps),:] = e1.copy()
if (mse[0] > 1.0) or (mse[1] > 1.0):
count_large_errors = count_large_errors + 1
continue
count_good = count_good + 1
print("MSE: %f,%f" % (mse[0],mse[1]))
# chi-square test statistics
# (alpha) probability of being less than the returned value: stats.chi2.ppf(alpha,df=Nsims)
if Ns < 2:
trials_processing.printSingleSim(tsim,xf,Pf,xk,name='ukf',save_flag=None,history_lines=True,draw_snapshots=False)
#trials_processing.errorParsing(e_sims,nees_history,'ukf','sims_01_bifurcation')
# write to file
# Ns, count_good, count_singular_covariance, count_large_errors, Qk[0,0], Ts
fname = 'ukf_data.txt'
FID = open(fname,'a')
FID.write("%d,%d,%d,%d,%g,%g\n" % (Ns,count_good,count_singular_covariance,count_large_errors,Qk[0,0],Ts))
FID.close()
"""
if Ns < 2:
fig1 = plt.figure()
ax = []
for k in range(4):
if k < 2:
nam = 'x' + str(k+1)
else:
nam = 'e' + str(k-1)
ax.append(fig1.add_subplot(2,2,k+1,ylabel=nam))
if k < 2:
ax[k].plot(tsim,xk[:,k],'b-')
ax[k].plot(tsim,xf[:,k],'m--')
if k == 0:
ax[k].plot(tsim,yk,'r--')
else:
ax[k].plot(tsim,xk[:,k-2]-xf[:,k-2])
ax[k].plot(tsim,3.0*np.sqrt(Pf[:,3*(k-2)]),'r--')
ax[k].plot(tsim,-3.0*np.sqrt(Pf[:,3*(k-2)]),'r--')
ax[k].grid()
fig1.show()
fig2 = plt.figure()
ax = []
ax.append(fig2.add_subplot(111,ylabel = 'nees metric'))
ax[0].plot(tsim,chi2)
ax[0].grid()
fig2.show()
trials_processing.errorParsing(e_sims,nees_history,'ukf',nameNow)
mse_tot = np.mean(np.power(e_sims,2.0),axis=0)
print("mse_tot: %f,%f" % (mse_tot[0],mse_tot[1]))
# get the mean NEES value versus simulation time across all sims
nees_mean = np.sum(nees_history,axis=1)/Ns
# get 95% confidence bounds for chi-sqaured... the df is the number of sims times the dimension of the state
chiUpper = stats.chi2.ppf(.975,2.0*Ns)/float(Ns)
chiLower = stats.chi2.ppf(.025,2.0*Ns)/float(Ns)
# plot the mean NEES with the 95% confidence bounds
fig2 = plt.figure(figsize=(6.0,3.37)) #figsize tuple is width, height
tilt = "UKF, Ts = %.2f, %d sims, " % (dt, Ns)
if nameBit == 0:
tilt = tilt + 'unforced'
if nameBit == 1:
#white-noise only
tilt = tilt + 'white-noise forcing'
if nameBit == 2:
tilt = tilt + 'cosine forcing'
if nameBit == 3:
#white-noise and cosine forcing
tilt = tilt + 'white-noise and cosine forcing'
ax = fig2.add_subplot(111,ylabel='mean NEES',title=tilt)
ax.plot(tsim,chiUpper*np.ones(nSteps),'r--')
ax.plot(tsim,chiLower*np.ones(nSteps),'r--')
ax.plot(tsim,nees_mean,'b-')
ax.grid()
fig2.show()
# save the figure
fig2.savefig('nees_ukf_' + nameNow + '.png')
# find fraction of inliers
l1 = (nees_mean < chiUpper).nonzero()[0]
l2 = (nees_mean > chiLower).nonzero()[0]
# get number of inliers
len_in = len(set(l1).intersection(l2))
# get number of super (above) liers (sic)
len_super = len((nees_mean > chiUpper).nonzero()[0])
# get number of sub-liers (below)
len_sub = len((nees_mean < chiLower).nonzero()[0])
print("Conservative (below 95%% bounds): %f" % (float(len_sub)/float(nSteps)))
print("Optimistic (above 95%% bounds): %f" % (float(len_super)/float(nSteps)))
# save metrics
FID = open('metrics_ukf_' + nameNow + '.txt','w')
FID.write("mse1,mse2,nees_below95,nees_above95\n")
FID.write("%f,%f,%f,%f\n" % (mse_tot[0],mse_tot[1],float(len_sub)/float(nSteps),float(len_super)/float(nSteps)))
FID.close()
# plot all NEES
fig = plt.figure(figsize=(6.0,3.37))
ax = fig.add_subplot(111,ylabel='NEES')
ax.plot(tsim,nees_history,'b-')
ax.grid()
fig.show()
raw_input("Return to quit")
"""
print("Leaving ukf_trials")
return
