plt.legend(loc=4, borderaxespad=0.0, prop={'size': 20}, frameon=False)
plt.tight_layout()
plt.show(block=True)
### instantiate an MCMC sampler
mcmc = MCMC(density, proposal_density, draw_from_proposal,
initial_point_mcmc)
# run the MCMC sample
mcmc.run(max_iter=10000, burning=1000)
# write the samples into a file
#mcmc.write("samples-N3-fric0.075-wNoise.dat")
# plotting the sampled friction coefficients
for idx, coef in enumerate(mcmc.density_samples):
pipe.get_lambda_average(coef)
plt.plot(pipe.mesh, pipe.lambda_avg)
pipe_true.get_lambda_average(true_friction)
plt.plot(pipe_true.mesh,
pipe_true.lambda_avg,
'--',
color="black",
linewidth=5.0,
label="True friction function")
plt.legend(loc=1, borderaxespad=0.0, prop={'size': 20}, frameon=False)
plt.yticks(fontsize=20)
plt.xticks(fontsize=20)
plt.xlabel("$x$", fontsize=24)
plt.ylabel("$\lambda(x)$", fontsize=24)
from UQuant.SemilinearSystem import SemiLinSystem
# build a pipe
pipe = SemiLinSystem(1.0, 5.0, 0.0, 1.0, 0.005, 7, 0.05)
# get the info of the pipe
pipe.info()
# check how pressure drop behaves when the friction coefficient is
# updated. Theoretically we have continuous dependence which can
# be seen also numerically.
coef = 0.0
for i in range(0, 100):
vec_c = [0.05 + coef, 0.01, 0.0, 0.04, 0.0, 0.005, 0.005]
pipe.run(vec_c)
pipe.get_lambda_average(vec_c)
pipe.get_presure_drop(time_instance=13)
if i % 10 == 1:
plt.plot(pipe.timeslices,
pipe.pressure_drop,
"-o",
label="cf = " + str(0.05 + coef))
coef += 0.001
print ">> Computation Done"
plt.legend(loc=2, borderaxespad=0.0)
plt.xticks([round(tn, 2) for tn in pipe.timeslices])
plt.xlabel("$t_n$", fontsize=24)
plt.ylabel("$\delta p_h(t_n)$", fontsize=24)
plt.tight_layout()
clusters = []
fig = plt.figure(figsize=(10, 5))
show_clusters = range(n_clusters)
n_show_clusters = len(show_clusters)
for idx, cluster in enumerate(show_clusters):
ax = fig.add_subplot(1, n_show_clusters, idx + 1)
plt.yticks(fontsize=18)
plt.xticks(fontsize=18, rotation=25)
plt.xlabel("$x$", fontsize=24)
mean_cluster.append(df.iloc[pred == cluster, :].mean().values)
pipe.get_lambda_average(mean_cluster[idx])
ax.plot(pipe.mesh,
pipe.lambda_avg,
label="$E(\Lambda_" + str(idx + 1) + ")(x)$")
pipe_true.get_lambda_average(true_friction)
ax.plot(pipe_true.mesh,
pipe_true.lambda_avg,
"--",
label="$\lambda_{true}(x)$")
#ax.legend(loc="upper left", prop={'size': 16}, frameon=False)
ax.set_aspect(aspect=6)
ax.legend(loc='upper left', bbox_to_anchor=(0.05, 1.275), fontsize=12)
if cluster != 0:
# df = pd.read_csv("tmp.dat", header=None)
# initial_point_mcmc = df.iloc[-1,0:-1].values
linestyles = ['-.', '-', '--', ':']
counter = 0
plt.style.use('grayscale')
for i in range(1, len(true_friction) + 1, 2):
tmp = true_friction[:i]
pipe_tmp = SemiLinSystem(c_sound, t_final, x_l, x_r, dx, len(tmp),
boundary_eps)
# get the info of the pipe
# pipe_tmp.info()
pipe_tmp.get_lambda_average(tmp)
#plt.plot(pipe.timeslices, pipe.pressure_drop, "o-")
if i in [1, 9, 11, 19, 25, 41]:
plt.plot(pipe_tmp.mesh,
pipe_tmp.lambda_avg,
linestyle=linestyles[counter % len(linestyles)],
label="$N=" + str(i / 2) + "$")
counter += 1
plt.legend(loc="best", prop={'size': 16}, frameon=False)
plt.yticks(fontsize=20)
plt.xticks(fontsize=20)
plt.xlabel("$x$", fontsize=24)
plt.ylabel("$\lambda^N(x)$", fontsize=24)
plt.tight_layout()
plt.plot(prob, label="MCMC samples")
plt.xlabel("$i$", fontsize=24)
plt.ylabel("$\propto \pi_y(\lambda_{(i)})$", fontsize=24)
plt.xticks(append(arange(0, len(prob), 7500), len(prob)),
rotation=25,
fontsize=18)
plt.yticks(fontsize=20)
plt.tight_layout()
plt.savefig("results/samples_posterior.pgf")
plt.show(block=False)
# plot the mean function, true and the initial sample
plt.figure()
for idx in sorted_prob_idx[0:5]:
pipe.get_lambda_average(df.loc[idx].values)
plt.plot(pipe.mesh,
pipe.lambda_avg,
label="$\lambda_{" + str(idx) + "}$")
# pipe.get_lambda_average(df.mean().values)
# Mean = pipe.lambda_avg
# plt.plot(pipe.mesh, Mean, label="$\mathrm{E}(\lambda)(x)$", linewidth=2)
pipe.get_lambda_average(initial_point_mcmc)
plt.plot(pipe.mesh,
pipe.lambda_avg,
label="$\lambda_{initial}(x)$",
linestyle="-.",
linewidth=2)