# use alternate mayavi plotting
MAYAVI_PLOTTING = True
# ============================================================
# PART B: Problem Setup
# ============================================================
# define initial multiindices
mis = [Multiindex(mis) for mis in MultiindexSet.createCompleteOrderSet(CONF_initial_Lambda, 1)]
#mis = [mis[0], mis[2]]
#mis = [mis[0]]
# setup domain and meshes
mesh0, boundaries, dim = SampleDomain.setupDomain(CONF_domain, initial_mesh_N=initial_mesh_N)
#meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=10, randref=(0.4, 0.3))
meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=0)
# define coefficient field
# NOTE: for proper treatment of corner points, see elasticity_residual_estimator
coeff_types = ("EF-square-cos", "EF-square-sin", "monomials", "constant")
from itertools import count
muparam = (CONF_mu, (0 for _ in count()))
coeff_field = SampleProblem.setupCF(coeff_types[CONF_coeff_type], decayexp=CONF_decay_exp, gamma=CONF_gamma,
freqscale=CONF_freq_scale, freqskip=CONF_freq_skip, rvtype="uniform", scale=CONF_coeff_scale, secondparam=muparam)
# setup boundary conditions and pde
pde, Dirichlet_boundary, uD, Neumann_boundary, g, f = SampleProblem.setupPDE(CONF_boundary_type, CONF_domain, CONF_problem_type, boundaries, coeff_field)
# define multioperator
def run_MC(opts, conf):
# propagate config values
_G = globals()
for sec in conf.keys():
if sec == "LOGGING":
continue
secconf = conf[sec]
for key, val in secconf.iteritems():
print "CONF_" + key + "= secconf['" + key + "'] =", secconf[key]
_G["CONF_" + key] = secconf[key]
# setup logging
_G["LOG_LEVEL"] = eval("logging." + conf["LOGGING"]["level"])
print "LOG_LEVEL = logging." + conf["LOGGING"]["level"]
setup_logging(LOG_LEVEL, logfile=CONF_experiment_name + "_MC-P{0}".format(CONF_FEM_degree))
# determine path of this module
path = os.path.dirname(__file__)
# ============================================================
# PART A: Setup Problem
# ============================================================
# get boundaries
mesh0, boundaries, dim = SampleDomain.setupDomain(CONF_domain, initial_mesh_N=CONF_initial_mesh_N)
# define coefficient field
coeff_types = ("EF-square-cos", "EF-square-sin", "monomials", "constant")
from itertools import count
if CONF_mu is not None:
muparam = (CONF_mu, (0 for _ in count()))
else:
muparam = None
coeff_field = SampleProblem.setupCF(coeff_types[CONF_coeff_type], decayexp=CONF_decay_exp, gamma=CONF_gamma,
freqscale=CONF_freq_scale, freqskip=CONF_freq_skip, rvtype="uniform", scale=CONF_coeff_scale, secondparam=muparam)
# setup boundary conditions and pde
# initial_mesh_N = CONF_initial_mesh_N
pde, Dirichlet_boundary, uD, Neumann_boundary, g, f = SampleProblem.setupPDE(CONF_boundary_type, CONF_domain, CONF_problem_type, boundaries, coeff_field)
# define multioperator
A = MultiOperator(coeff_field, pde.assemble_operator, pde.assemble_operator_inner_dofs)
# ============================================================
# PART B: Import Solution
# ============================================================
import pickle
PATH_SOLUTION = os.path.join(opts.basedir, CONF_experiment_name)
FILE_SOLUTION = 'SFEM2-SOLUTIONS-P{0}.pkl'.format(CONF_FEM_degree)
FILE_STATS = 'SIM2-STATS-P{0}.pkl'.format(CONF_FEM_degree)
print "LOADING solutions from %s" % os.path.join(PATH_SOLUTION, FILE_SOLUTION)
logger.info("LOADING solutions from %s" % os.path.join(PATH_SOLUTION, FILE_SOLUTION))
# load solutions
with open(os.path.join(PATH_SOLUTION, FILE_SOLUTION), 'rb') as fin:
w_history = pickle.load(fin)
# load simulation data
logger.info("LOADING statistics from %s" % os.path.join(PATH_SOLUTION, FILE_STATS))
with open(os.path.join(PATH_SOLUTION, FILE_STATS), 'rb') as fin:
sim_stats = pickle.load(fin)
logger.info("active indices of w after initialisation: %s", w_history[-1].active_indices())
# ============================================================
# PART C: MC Error Sampling
# ============================================================
# determine reference setting
ref_mesh, ref_Lambda = generate_reference_setup(PATH_SOLUTION)
MC_N = CONF_N
MC_HMAX = CONF_maxh
if CONF_runs > 0:
# determine reference mesh
w = w_history[-1]
# ref_mesh = w.basis.basis.mesh
for _ in range(CONF_ref_mesh_refine):
ref_mesh = refine(ref_mesh)
# TODO: the following association with the sampling order does not make too much sense...
ref_maxm = CONF_sampling_order if CONF_sampling_order > 0 else max(len(mu) for mu in ref_Lambda) + CONF_sampling_order_increase
stored_rv_samples = []
for i, w in enumerate(w_history):
# if i == 0:
# continue
# memory usage info
import resource
logger.info("\n======================================\nMEMORY USED: " + str(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) + "\n======================================\n")
logger.info("================>>> MC error sampling for w[%i] (of %i) on %i cells with maxm %i <<<================" % (i, len(w_history), ref_mesh.num_cells(), ref_maxm))
MC_start = 0
old_stats = sim_stats[i]
if opts.continueMC:
try:
MC_start = sim_stats[i]["MC-N"]
logger.info("CONTINUING MC of %s for solution (iteration) %s of %s", PATH_SOLUTION, i, len(w_history))
except:
logger.info("STARTING MC of %s for solution (iteration) %s of %s", PATH_SOLUTION, i, len(w_history))
if MC_start <= 0:
sim_stats[i]["MC-N"] = 0
sim_stats[i]["MC-ERROR-L2"] = 0
sim_stats[i]["MC-ERROR-H1A"] = 0
# sim_stats[i]["MC-ERROR-L2_a0"] = 0
# sim_stats[i]["MC-ERROR-H1_a0"] = 0
MC_RUNS = max(CONF_runs - MC_start, 0)
if MC_RUNS > 0:
logger.info("STARTING %s MC RUNS", MC_RUNS)
# L2err, H1err, L2err_a0, H1err_a0, N = sample_error_mc(w, pde, A, coeff_field, mesh0, ref_maxm, MC_RUNS, MC_N, MC_HMAX)
L2err, H1err, L2err_a0, H1err_a0, N = sample_error_mc(w, pde, A, coeff_field, ref_mesh, ref_maxm, MC_RUNS, MC_N, MC_HMAX, stored_rv_samples, CONF_quadrature_degree)
# combine current and previous results
sim_stats[i]["MC-N"] = N + old_stats["MC-N"]
sim_stats[i]["MC-ERROR-L2"] = (L2err * N + old_stats["MC-ERROR-L2"]) / sim_stats[i]["MC-N"]
sim_stats[i]["MC-ERROR-H1A"] = (H1err * N + old_stats["MC-ERROR-H1A"]) / sim_stats[i]["MC-N"]
# sim_stats[i]["MC-ERROR-L2_a0"] = (L2err_a0 * N + old_stats["MC-ERRORL2_a0"]) / sim_stats[i]["MC-N"]
# sim_stats[i]["MC-ERROR-H1A_a0"] = (H1err_a0 * N + old_stats["MC-ERROR-H1A_a0"]) / sim_stats[i]["MC-N"]
print "MC-ERROR-H1A (N:%i) = %f" % (sim_stats[i]["MC-N"], sim_stats[i]["MC-ERROR-H1A"])
else:
logger.info("SKIPPING MC RUN since sufficiently many samples are available")
# ============================================================
# PART D: Export Updated Data and Plotting
# ============================================================
# save updated data
if opts.saveData:
# save updated statistics
print "SAVING statistics into %s" % os.path.join(PATH_SOLUTION, FILE_STATS)
print sim_stats[-1].keys()
logger.info("SAVING statistics into %s" % os.path.join(PATH_SOLUTION, FILE_STATS))
with open(os.path.join(PATH_SOLUTION, FILE_STATS), 'wb') as fout:
pickle.dump(sim_stats, fout)
# plot residuals
if opts.plotEstimator and len(sim_stats) > 1:
try:
from matplotlib.pyplot import figure, show, legend
X = [s["DOFS"] for s in sim_stats]
err_L2 = [s["MC-ERROR-L2"] for s in sim_stats]
err_H1A = [s["MC-ERROR-H1A"] for s in sim_stats]
err_est = [s["ERROR-EST"] for s in sim_stats]
err_res = [s["ERROR-RES"] for s in sim_stats]
err_tail = [s["ERROR-TAIL"] for s in sim_stats]
mi = [s["MI"] for s in sim_stats]
num_mi = [len(m) for m in mi]
eff_H1A = [est / err for est, err in zip(err_est, err_H1A)]
# --------
# figure 1
# --------
fig1 = figure()
fig1.suptitle("residual estimator")
ax = fig1.add_subplot(111)
if REFINEMENT["TAIL"]:
ax.loglog(X, num_mi, '--y+', label='active mi')
ax.loglog(X, eff_H1A, '--yo', label='efficiency')
ax.loglog(X, err_L2, '-.b>', label='L2 error')
ax.loglog(X, err_H1A, '-.r>', label='H1A error')
ax.loglog(X, err_est, '-g<', label='error estimator')
ax.loglog(X, err_res, '-.cx', label='residual')
ax.loglog(X, err_tail, '-.m>', label='tail')
legend(loc='upper right')
print "error L2", err_L2
print "error H1A", err_H1A
print "EST", err_est
print "RES", err_res
print "TAIL", err_tail
show() # this invalidates the figure instances...
except:
import traceback
print traceback.format_exc()
logger.info("skipped plotting since matplotlib is not available...")
def run_SFEM(opts, conf):
# propagate config values
for sec in conf.keys():
if sec == "LOGGING":
continue
secconf = conf[sec]
for key, val in secconf.iteritems():
print "CONF_" + key + "= secconf['" + key + "'] =", secconf[key]
exec "CONF_" + key + "= secconf['" + key + "']"
# setup logging
print "LOG_LEVEL = logging." + conf["LOGGING"]["level"]
exec "LOG_LEVEL = logging." + conf["LOGGING"]["level"]
setup_logging(LOG_LEVEL, logfile=CONF_experiment_name + "_SFEM")
# determine path of this module
path = os.path.dirname(__file__)
# ============================================================
# PART A: Simulation Options
# ============================================================
# flags for residual, projection, new mi refinement
REFINEMENT = {"RES":CONF_refine_residual, "PROJ":CONF_refine_projection, "MI":CONF_refine_Lambda}
# ============================================================
# PART B: Problem Setup
# ============================================================
# define initial multiindices
mis = [Multiindex(mis) for mis in MultiindexSet.createCompleteOrderSet(CONF_initial_Lambda, 1)]
# setup domain and meshes
mesh0, boundaries, dim = SampleDomain.setupDomain(CONF_domain, initial_mesh_N=CONF_initial_mesh_N)
#meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=10, randref=(0.4, 0.3))
meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=0)
# define coefficient field
# NOTE: for proper treatment of corner points, see elasticity_residual_estimator
coeff_types = ("EF-square-cos", "EF-square-sin", "monomials", "constant")
from itertools import count
if CONF_mu is not None:
muparam = (CONF_mu, (0 for _ in count()))
else:
muparam = None
coeff_field = SampleProblem.setupCF(coeff_types[CONF_coeff_type], decayexp=CONF_decay_exp, gamma=CONF_gamma,
freqscale=CONF_freq_scale, freqskip=CONF_freq_skip, rvtype="uniform", scale=CONF_coeff_scale, secondparam=muparam)
# setup boundary conditions and pde
pde, Dirichlet_boundary, uD, Neumann_boundary, g, f = SampleProblem.setupPDE(CONF_boundary_type, CONF_domain, CONF_problem_type, boundaries, coeff_field)
# define multioperator
A = MultiOperator(coeff_field, pde.assemble_operator, pde.assemble_operator_inner_dofs, assembly_type=eval("ASSEMBLY_TYPE." + CONF_assembly_type))
# setup initial solution multivector
w = SampleProblem.setupMultiVector(dict([(mu, m) for mu, m in zip(mis, meshes)]), functools.partial(setup_vector, pde=pde, degree=CONF_FEM_degree))
logger.info("active indices of w after initialisation: %s", w.active_indices())
sim_stats = None
w_history = []
if opts.continueSFEM:
try:
logger.info("CONTINUIING EXPERIMENT: loading previous data of %s...", CONF_experiment_name)
import pickle
LOAD_SOLUTION = os.path.join(opts.basedir, CONF_experiment_name)
logger.info("loading solutions from %s" % os.path.join(LOAD_SOLUTION, 'SFEM-SOLUTIONS.pkl'))
# load solutions
with open(os.path.join(LOAD_SOLUTION, 'SFEM-SOLUTIONS.pkl'), 'rb') as fin:
w_history = pickle.load(fin)
# convert to MultiVectorWithProjection
for i, mv in enumerate(w_history):
w_history[i] = MultiVectorWithProjection(cache_active=True, multivector=w_history[i])
# load simulation data
logger.info("loading statistics from %s" % os.path.join(LOAD_SOLUTION, 'SIM-STATS.pkl'))
with open(os.path.join(LOAD_SOLUTION, 'SIM-STATS.pkl'), 'rb') as fin:
sim_stats = pickle.load(fin)
logger.info("active indices of w after initialisation: %s", w_history[-1].active_indices())
w0 = w_history[-1]
except:
logger.warn("FAILED LOADING EXPERIMENT %s --- STARTING NEW DATA", CONF_experiment_name)
w0 = w
else:
w0 = w
# ============================================================
# PART C: Adaptive Algorithm
# ============================================================
# refinement loop
# ===============
w, sim_stats = AdaptiveSolver(A, coeff_field, pde, mis, w0, mesh0, CONF_FEM_degree, gamma=CONF_gamma, cQ=CONF_cQ, ceta=CONF_ceta,
# marking parameters
theta_eta=CONF_theta_eta, theta_zeta=CONF_theta_zeta, min_zeta=CONF_min_zeta,
maxh=CONF_maxh, newmi_add_maxm=CONF_newmi_add_maxm, theta_delta=CONF_theta_delta,
marking_strategy=CONF_marking_strategy, max_Lambda_frac=CONF_max_Lambda_frac,
# residual error evaluation
quadrature_degree=CONF_quadrature_degree,
# projection error evaluation
projection_degree_increase=CONF_projection_degree_increase, refine_projection_mesh=CONF_refine_projection_mesh,
# pcg solver
pcg_eps=CONF_pcg_eps, pcg_maxiter=CONF_pcg_maxiter,
# adaptive algorithm threshold
error_eps=CONF_error_eps,
# refinements
max_refinements=CONF_iterations, max_dof=CONF_max_dof,
do_refinement=REFINEMENT, do_uniform_refinement=CONF_uniform_refinement,
w_history=w_history,
sim_stats=sim_stats)
from operator import itemgetter
active_mi = [(mu, w[mu]._fefunc.function_space().mesh().num_cells()) for mu in w.active_indices()]
active_mi = sorted(active_mi, key=itemgetter(1), reverse=True)
logger.info("==== FINAL MESHES ====")
for mu in active_mi:
logger.info("--- %s has %s cells", mu[0], mu[1])
print "ACTIVE MI:", active_mi
print
# memory usage info
import resource
logger.info("\n======================================\nMEMORY USED: " + str(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) + "\n======================================\n")
# ============================================================
# PART D: Export of Solutions and Simulation Data
# ============================================================
# flag for final solution export
if opts.saveData:
import pickle
SAVE_SOLUTION = os.path.join(opts.basedir, CONF_experiment_name)
try:
os.makedirs(SAVE_SOLUTION)
except:
pass
logger.info("saving solutions into %s" % os.path.join(SAVE_SOLUTION, 'SFEM-SOLUTIONS.pkl'))
# save solutions
with open(os.path.join(SAVE_SOLUTION, 'SFEM-SOLUTIONS.pkl'), 'wb') as fout:
pickle.dump(w_history, fout)
# save simulation data
sim_stats[0]["OPTS"] = opts
sim_stats[0]["CONF"] = conf
logger.info("saving statistics into %s" % os.path.join(SAVE_SOLUTION, 'SIM-STATS.pkl'))
with open(os.path.join(SAVE_SOLUTION, 'SIM-STATS.pkl'), 'wb') as fout:
pickle.dump(sim_stats, fout)
# ============================================================
# PART E: Plotting
# ============================================================
# plot residuals
if opts.plotEstimator and len(sim_stats) > 1:
try:
from matplotlib.pyplot import figure, show, legend
X = [s["DOFS"] for s in sim_stats]
print "DOFS", X
L2 = [s["L2"] for s in sim_stats]
H1 = [s["H1"] for s in sim_stats]
errest = [sqrt(s["EST"]) for s in sim_stats]
res_part = [s["RES-PART"] for s in sim_stats]
proj_part = [s["PROJ-PART"] for s in sim_stats]
pcg_part = [s["PCG-PART"] for s in sim_stats]
_reserrmu = [s["RES-mu"] for s in sim_stats]
_projerrmu = [s["PROJ-mu"] for s in sim_stats]
proj_max_zeta = [s["PROJ-MAX-ZETA"] for s in sim_stats]
proj_max_inactive_zeta = [s["PROJ-MAX-INACTIVE-ZETA"] for s in sim_stats]
try:
proj_inactive_zeta = sorted([v for v in sim_stats[-2]["PROJ-INACTIVE-ZETA"].values()], reverse=True)
except:
proj_inactive_zeta = None
mi = [s["MI"] for s in sim_stats]
num_mi = [len(m) for m in mi]
time_pcg = [s["TIME-PCG"] for s in sim_stats]
time_estimator = [s["TIME-ESTIMATOR"] for s in sim_stats]
time_inactive_mi = [s["TIME-INACTIVE-MI"] for s in sim_stats]
time_marking = [s["TIME-MARKING"] for s in sim_stats]
reserrmu = defaultdict(list)
for rem in _reserrmu:
for mu, v in rem:
reserrmu[mu].append(v)
projerrmu = defaultdict(list)
for pem in _projerrmu:
for mu, v in pem:
projerrmu[mu].append(v)
print "errest", errest
# --------
# figure 2
# --------
fig2 = figure()
fig2.suptitle("error estimator")
ax = fig2.add_subplot(111)
ax.loglog(X, errest, '-g<', label='error estimator')
legend(loc='upper right')
# --------
# figure 3a
# --------
if opts.plotEstimatorAll:
max_mu_plotting = 7
fig3 = figure()
fig3.suptitle("residual contributions")
ax = fig3.add_subplot(111)
for i, muv in enumerate(reserrmu.iteritems()):
mu, v = muv
if i < max_mu_plotting:
mu, v = muv
ms = str(mu)
ms = ms[ms.find('=') + 1:-1]
ax.loglog(X[-len(v):], v, '-g<', label=ms)
legend(loc='upper right')
# --------
# figure 3b
# --------
if opts.plotEstimatorAll:
fig3b = figure()
fig3b.suptitle("projection contributions")
ax = fig3b.add_subplot(111)
for i, muv in enumerate(projerrmu.iteritems()):
mu, v = muv
if max(v) > 1e-10 and i < max_mu_plotting:
ms = str(mu)
ms = ms[ms.find('=') + 1:-1]
ax.loglog(X[-len(v):], v, '-g<', label=ms)
legend(loc='upper right')
# --------
# figure 4
# --------
if opts.plotEstimatorAll:
fig4 = figure()
fig4.suptitle("projection $\zeta$")
ax = fig4.add_subplot(111)
ax.loglog(X[1:], proj_max_zeta[1:], '-g<', label='max active $\zeta$')
ax.loglog(X[1:], proj_max_inactive_zeta[1:], '-b^', label='max inactive $\zeta$')
legend(loc='upper right')
# --------
# figure 5
# --------
fig5 = figure()
fig5.suptitle("timings")
ax = fig5.add_subplot(111)
ax.loglog(X, time_pcg, '-g<', label='pcg')
ax.loglog(X, time_estimator, '-b^', label='estimator')
ax.loglog(X, time_inactive_mi, '-c+', label='inactive_mi')
ax.loglog(X, time_marking, '-ro', label='marking')
legend(loc='upper right')
# --------
# figure 6
# --------
if opts.plotEstimatorAll:
fig6 = figure()
fig6.suptitle("projection error")
ax = fig6.add_subplot(111)
ax.loglog(X[1:], proj_part[1:], '-.m>', label='projection part')
legend(loc='upper right')
# --------
# figure 7
# --------
if opts.plotEstimatorAll and proj_inactive_zeta is not None:
fig7 = figure()
fig7.suptitle("inactive multiindex $\zeta$")
ax = fig7.add_subplot(111)
ax.loglog(range(len(proj_inactive_zeta)), proj_inactive_zeta, '-.m>', label='inactive $\zeta$')
legend(loc='lower right')
# --------
# figure 1
# --------
fig1 = figure()
fig1.suptitle("residual estimator")
ax = fig1.add_subplot(111)
if REFINEMENT["MI"]:
ax.loglog(X, num_mi, '--y+', label='active mi')
ax.loglog(X, errest, '-g<', label='error estimator')
ax.loglog(X, res_part, '-.cx', label='residual part')
ax.loglog(X[1:], proj_part[1:], '-.m>', label='projection part')
ax.loglog(X, pcg_part, '-.b>', label='pcg part')
legend(loc='upper right')
show() # this invalidates the figure instances...
except:
import traceback
print traceback.format_exc()
logger.info("skipped plotting since matplotlib is not available...")
# plot final meshes
if opts.plotMesh:
USE_MAYAVI = Plotter.hasMayavi() and False
w = w_history[-1]
for mu, vec in w.iteritems():
if USE_MAYAVI:
# mesh
# Plotter.figure(bgcolor=(1, 1, 1))
# mesh = vec.basis.mesh
# Plotter.plotMesh(mesh.coordinates(), mesh.cells(), representation='mesh')
# Plotter.axes()
# Plotter.labels()
# Plotter.title(str(mu))
# function
Plotter.figure(bgcolor=(1, 1, 1))
mesh = vec.basis.mesh
Plotter.plotMesh(mesh.coordinates(), mesh.cells(), vec.coeffs)
Plotter.axes()
Plotter.labels()
Plotter.title(str(mu))
else:
viz_mesh = plot(vec.basis.mesh, title="mesh " + str(mu), interactive=False)
# if SAVE_SOLUTION != '':
# viz_mesh.write_png(SAVE_SOLUTION + '/mesh' + str(mu) + '.png')
# viz_mesh.write_ps(SAVE_SOLUTION + '/mesh' + str(mu), format='pdf')
# vec.plot(title=str(mu), interactive=False)
if USE_MAYAVI:
Plotter.show(stop=True)
Plotter.close(allfig=True)
else:
interactive()
# plot sample solution
if opts.plotSolution:
w = w_history[-1]
# get random field sample and evaluate solution (direct and parametric)
RV_samples = coeff_field.sample_rvs()
ref_maxm = w_history[-1].max_order
sub_spaces = w[Multiindex()].basis.num_sub_spaces
degree = w[Multiindex()].basis.degree
maxh = min(w[Multiindex()].basis.minh / 4, CONF_max_h)
maxh = w[Multiindex()].basis.minh
projection_basis = get_projection_basis(mesh0, maxh=maxh, degree=degree, sub_spaces=sub_spaces)
sample_sol_param = compute_parametric_sample_solution(RV_samples, coeff_field, w, projection_basis)
sample_sol_direct = compute_direct_sample_solution(pde, RV_samples, coeff_field, A, ref_maxm, projection_basis)
sol_variance = compute_solution_variance(coeff_field, w, projection_basis)
# plot
print sub_spaces
if sub_spaces == 0:
viz_p = plot(sample_sol_param._fefunc, title="parametric solution")
viz_d = plot(sample_sol_direct._fefunc, title="direct solution")
if ref_maxm > 0:
viz_v = plot(sol_variance._fefunc, title="solution variance")
# debug---
if not True:
for mu in w.active_indices():
for i, wi in enumerate(w_history):
if i == len(w_history) - 1 or True:
plot(wi[mu]._fefunc, title="parametric solution " + str(mu) + " iteration " + str(i))
# plot(wi[mu]._fefunc.function_space().mesh(), title="parametric solution " + str(mu) + " iteration " + str(i), axes=True)
interactive()
# ---debug
# for mu in w.active_indices():
# plot(w[mu]._fefunc, title="parametric solution " + str(mu))
else:
mesh_param = sample_sol_param._fefunc.function_space().mesh()
mesh_direct = sample_sol_direct._fefunc.function_space().mesh()
wireframe = True
viz_p = plot(sample_sol_param._fefunc, title="parametric solution", mode="displacement", mesh=mesh_param, wireframe=wireframe)#, rescale=False)
viz_d = plot(sample_sol_direct._fefunc, title="direct solution", mode="displacement", mesh=mesh_direct, wireframe=wireframe)#, rescale=False)
# for mu in w.active_indices():
# viz_p = plot(w[mu]._fefunc, title="parametric solution: " + str(mu), mode="displacement", mesh=mesh_param, wireframe=wireframe)
interactive()
if opts.plotFlux:
w = w_history[-1]
# get random field sample and evaluate solution (direct and parametric)
RV_samples = coeff_field.sample_rvs()
ref_maxm = w_history[-1].max_order
sub_spaces = w[Multiindex()].basis.num_sub_spaces
degree = w[Multiindex()].basis.degree
maxh = min(w[Multiindex()].basis.minh / 4, CONF_max_h)
maxh = w[Multiindex()].basis.minh
projection_basis = get_projection_basis(mesh0, maxh=maxh, degree=degree, sub_spaces=sub_spaces)
vec_projection_basis = get_projection_basis(mesh0, maxh=maxh, degree=degree, sub_spaces=2)
sample_sol_param = compute_parametric_sample_solution(RV_samples, coeff_field, w, projection_basis)
sample_sol_direct = compute_direct_sample_solution(pde, RV_samples, coeff_field, A, ref_maxm, projection_basis)
sol_variance = compute_solution_variance(coeff_field, w, projection_basis)
sol_param_flux = compute_solution_flux(pde, RV_samples, coeff_field, sample_sol_param, ref_maxm, projection_basis, vec_projection_basis)
sol_direct_flux = compute_solution_flux(pde, RV_samples, coeff_field, sample_sol_direct, ref_maxm, projection_basis, vec_projection_basis)
# plot
if sub_spaces == 0:
#viz_p = plot(sol_param_flux._fefunc, title="parametric solution flux")
flux_x, flux_y = sol_param_flux._fefunc.split(deepcopy=True)
viz_x = plot(flux_x, title="parametric solution flux x")
viz_y = plot(flux_y, title="parametric solution flux y")
flux_x, flux_y = sol_direct_flux._fefunc.split(deepcopy=True)
viz_x = plot(flux_x, title="direct solution flux x")
viz_y = plot(flux_y, title="direct solution flux y")
else:
raise Exception("not implemented");
interactive()
elif type == 'H':
assert False
#J = MultiindexSet.createCompleteOrderSet(M, p2).arr
#H = evaluate_Hermite_triple(I, I, J)
#L = [L[:, :, k] for k in range(L.shape[2])]
return L
def prepare_vectors(J, basis):
return [basis.new_vector().array for _ in range(J)]
# A setup problem
# ===============
# setup domain and meshes
mesh, boundaries, dim = SampleDomain.setupDomain("square", initial_mesh_N=10)
mesh = SampleProblem.setupMesh(mesh, num_refine=0)
# define coefficient field
coeff_field = SampleProblem.setupCF("EF-square-cos", decayexp=2, gamma=0.9, freqscale=1, freqskip=0, rvtype="uniform", scale=1)
# setup boundary conditions and pde
pde, Dirichlet_boundary, uD, Neumann_boundary, g, f = SampleProblem.setupPDE(2, "square", 0, boundaries, coeff_field)
# B setup tensor operator
# =======================
# setup deterministic operators
M, degree = 3, 1
K, FS = prepare_deterministic_operators(pde, coeff_field, M, mesh, degree)
def run_SFEM(opts, conf):
# propagate config values
_G = globals()
for sec in conf.keys():
if sec == "LOGGING":
continue
secconf = conf[sec]
for key, val in secconf.iteritems():
print "CONF_" + key + "= secconf['" + key + "'] =", secconf[key]
_G["CONF_" + key] = secconf[key]
# setup logging
_G["LOG_LEVEL"] = eval("logging." + conf["LOGGING"]["level"])
exec "LOG_LEVEL = logging." + conf["LOGGING"]["level"]
setup_logging(LOG_LEVEL, logfile=CONF_experiment_name + "_SFEM-P{0}".format(CONF_FEM_degree))
# determine path of this module
path = os.path.dirname(__file__)
# ============================================================
# PART A: Simulation Options
# ============================================================
# flags for residual and tail refinement
REFINEMENT = {"RES":CONF_refine_residual, "TAIL":CONF_refine_tail, "OSC":CONF_refine_osc}
# ============================================================
# PART B: Problem Setup
# ============================================================
# define initial multiindices
mis = [Multiindex(mis) for mis in MultiindexSet.createCompleteOrderSet(CONF_initial_Lambda, 1)]
# setup domain and meshes
mesh0, boundaries, dim = SampleDomain.setupDomain(CONF_domain, initial_mesh_N=CONF_initial_mesh_N)
#meshes = SampleProblem.setupMesh(mesh0, num_refine=10, randref=(0.4, 0.3))
mesh0 = SampleProblem.setupMesh(mesh0, num_refine=0)
# define coefficient field
# NOTE: for proper treatment of corner points, see elasticity_residual_estimator
coeff_types = ("EF-square-cos", "EF-square-sin", "monomials", "constant")
from itertools import count
if CONF_mu is not None:
muparam = (CONF_mu, (0 for _ in count()))
else:
muparam = None
coeff_field = SampleProblem.setupCF(coeff_types[CONF_coeff_type], decayexp=CONF_decay_exp, gamma=CONF_gamma,
freqscale=CONF_freq_scale, freqskip=CONF_freq_skip, rvtype="uniform", scale=CONF_coeff_scale, secondparam=muparam)
# setup boundary conditions and pde
pde, Dirichlet_boundary, uD, Neumann_boundary, g, f = SampleProblem.setupPDE(CONF_boundary_type, CONF_domain, CONF_problem_type, boundaries, coeff_field)
# define multioperator
A = MultiOperator(coeff_field, pde.assemble_operator, pde.assemble_operator_inner_dofs)
# setup initial solution multivector
w = SampleProblem.setupMultiVector(mis, pde, mesh0, CONF_FEM_degree)
logger.info("active indices of w after initialisation: %s", w.active_indices())
sim_stats = None
w_history = []
PATH_SOLUTION = os.path.join(opts.basedir, CONF_experiment_name)
try:
os.makedirs(PATH_SOLUTION)
except:
pass
FILE_SOLUTION = 'SFEM2-SOLUTIONS-P{0}.pkl'.format(CONF_FEM_degree)
FILE_STATS = 'SIM2-STATS-P{0}.pkl'.format(CONF_FEM_degree)
if opts.continueSFEM:
try:
logger.info("CONTINUING EXPERIMENT: loading previous data of %s...", CONF_experiment_name)
import pickle
logger.info("loading solutions from %s" % os.path.join(PATH_SOLUTION, FILE_SOLUTION))
# load solutions
with open(os.path.join(PATH_SOLUTION, FILE_SOLUTION), 'rb') as fin:
w_history = pickle.load(fin)
# convert to MultiVectorWithProjection
for i, mv in enumerate(w_history):
w_history[i] = MultiVectorSharedBasis(multivector=w_history[i])
# load simulation data
logger.info("loading statistics from %s" % os.path.join(PATH_SOLUTION, FILE_STATS))
with open(os.path.join(PATH_SOLUTION, FILE_STATS), 'rb') as fin:
sim_stats = pickle.load(fin)
logger.info("active indices of w after initialisation: %s", w_history[-1].active_indices())
w0 = w_history[-1]
except:
logger.warn("FAILED LOADING EXPERIMENT %s --- STARTING NEW DATA", CONF_experiment_name)
w0 = w
else:
w0 = w
# ============================================================
# PART C: Adaptive Algorithm
# ============================================================
# refinement loop
# ===============
w, sim_stats = AdaptiveSolver(A, coeff_field, pde, mis, w0, mesh0, CONF_FEM_degree,
# marking parameters
rho=CONF_rho, # tail factor
theta_x=CONF_theta_x, # residual marking bulk parameter
theta_y=CONF_theta_y, # tail bound marking bulk paramter
maxh=CONF_maxh, # maximal mesh width for coefficient maximum norm evaluation
add_maxm=CONF_add_maxm, # maximal search length for new new
# error estimator evaluation
estimator_type=CONF_estimator_type,
quadrature_degree=CONF_quadrature_degree,
# pcg solver
pcg_eps=CONF_pcg_eps, pcg_maxiter=CONF_pcg_maxiter,
# adaptive algorithm threshold
error_eps=CONF_error_eps,
# refinements
max_refinements=CONF_iterations, max_dof=CONF_max_dof,
do_refinement=REFINEMENT, do_uniform_refinement=CONF_uniform_refinement, refine_osc_factor=CONF_refine_osc_factor,
w_history=w_history,
sim_stats=sim_stats)
from operator import itemgetter
active_mi = [(mu, w[mu]._fefunc.function_space().mesh().num_cells()) for mu in w.active_indices()]
active_mi = sorted(active_mi, key=itemgetter(1), reverse=True)
logger.info("==== FINAL MESHES ====")
for mu in active_mi:
logger.info("--- %s has %s cells", mu[0], mu[1])
print "ACTIVE MI:", active_mi
print
# memory usage info
import resource
logger.info("\n======================================\nMEMORY USED: " + str(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) + "\n======================================\n")
# ============================================================
# PART D: Export of Solutions and Simulation Data
# ============================================================
# flag for final solution export
if opts.saveData:
import pickle
try:
os.makedirs(PATH_SOLUTION)
except:
pass
logger.info("saving solutions into %s" % os.path.join(PATH_SOLUTION, FILE_SOLUTION))
# save solutions
with open(os.path.join(PATH_SOLUTION, FILE_SOLUTION), 'wb') as fout:
pickle.dump(w_history, fout)
# save simulation data
sim_stats[0]["OPTS"] = opts
sim_stats[0]["CONF"] = conf
logger.info("saving statistics into %s" % os.path.join(PATH_SOLUTION, FILE_STATS))
with open(os.path.join(PATH_SOLUTION, FILE_STATS), 'wb') as fout:
pickle.dump(sim_stats, fout)
# ============================================================
# PART E: Plotting
# ============================================================
# plot residuals
if opts.plotEstimator and len(sim_stats) > 1:
try:
from matplotlib.pyplot import figure, show, legend
X = [s["DOFS"] for s in sim_stats]
print "DOFS", X
err_est = [s["ERROR-EST"] for s in sim_stats]
err_res = [s["ERROR-RES"] for s in sim_stats]
err_tail = [s["ERROR-TAIL"] for s in sim_stats]
res_L2 = [s["RESIDUAL-L2"] for s in sim_stats]
res_H1A = [s["RESIDUAL-H1A"] for s in sim_stats]
mi = [s["MI"] for s in sim_stats]
num_mi = [len(m) for m in mi]
# --------
# figure 1
# --------
fig1 = figure()
fig1.suptitle("residual estimator")
ax = fig1.add_subplot(111)
if REFINEMENT["TAIL"]:
ax.loglog(X, num_mi, '--y+', label='active mi')
ax.loglog(X, err_est, '-g<', label='error estimator')
ax.loglog(X, err_res, '-.cx', label='residual')
ax.loglog(X, err_tail, '-.m>', label='tail')
legend(loc='upper right')
print "RESIDUAL L2", res_L2
print "RESIDUAL H1A", res_H1A
print "EST", err_est
print "RES", err_res
print "TAIL", err_tail
show() # this invalidates the figure instances...
except:
import traceback
print traceback.format_exc()
logger.info("skipped plotting since matplotlib is not available...")
# plot final meshes
if opts.plotMesh:
w = w_history[-1]
viz_mesh = plot(w.basis.basis.mesh, title="shared mesh", interactive=False)
interactive()
# plot sample solution
if opts.plotSolution:
w = w_history[-1]
# get random field sample and evaluate solution (direct and parametric)
RV_samples = coeff_field.sample_rvs()
ref_maxm = w_history[-1].max_order
sub_spaces = w[Multiindex()].basis.num_sub_spaces
degree = w[Multiindex()].basis.degree
maxh = min(w[Multiindex()].basis.minh / 4, CONF_maxh)
maxh = w[Multiindex()].basis.minh
projection_basis = get_projection_basis(mesh0, maxh=maxh, degree=degree, sub_spaces=sub_spaces)
sample_sol_param = compute_parametric_sample_solution(RV_samples, coeff_field, w, projection_basis)
sample_sol_direct = compute_direct_sample_solution(pde, RV_samples, coeff_field, A, ref_maxm, projection_basis)
sol_variance = compute_solution_variance(coeff_field, w, projection_basis)
# plot
print sub_spaces
if sub_spaces == 0:
viz_p = plot(sample_sol_param._fefunc, title="parametric solution")
viz_d = plot(sample_sol_direct._fefunc, title="direct solution")
if ref_maxm > 0:
viz_v = plot(sol_variance._fefunc, title="solution variance")
else:
mesh_param = sample_sol_param._fefunc.function_space().mesh()
mesh_direct = sample_sol_direct._fefunc.function_space().mesh()
wireframe = True
viz_p = plot(sample_sol_param._fefunc, title="parametric solution", mode="displacement", mesh=mesh_param, wireframe=wireframe)#, rescale=False)
viz_d = plot(sample_sol_direct._fefunc, title="direct solution", mode="displacement", mesh=mesh_direct, wireframe=wireframe)#, rescale=False)
interactive()
def run_MC(opts, conf):
# propagate config values
_G = globals()
for sec in conf.keys():
if sec == "LOGGING":
continue
secconf = conf[sec]
for key, val in secconf.iteritems():
print "CONF_" + key + "= secconf['" + key + "'] =", secconf[key]
_G["CONF_" + key] = secconf[key]
# exec "CONF_" + key + "= secconf['" + key + "']"
# setup logging
_G["LOG_LEVEL"] = eval("logging." + conf["LOGGING"]["level"])
print "LOG_LEVEL = logging." + conf["LOGGING"]["level"]
# exec "LOG_LEVEL = logging." + conf["LOGGING"]["level"]
setup_logging(LOG_LEVEL, logfile=CONF_experiment_name + "_MC")
# determine path of this module
path = os.path.dirname(__file__)
# ============================================================
# PART A: Setup Problem
# ============================================================
# get boundaries
mesh0, boundaries, dim = SampleDomain.setupDomain(CONF_domain, initial_mesh_N=CONF_initial_mesh_N)
# define coefficient field
coeff_types = ("EF-square-cos", "EF-square-sin", "monomials", "constant")
from itertools import count
if CONF_mu is not None:
muparam = (CONF_mu, (0 for _ in count()))
else:
muparam = None
coeff_field = SampleProblem.setupCF(coeff_types[CONF_coeff_type], decayexp=CONF_decay_exp, gamma=CONF_gamma,
freqscale=CONF_freq_scale, freqskip=CONF_freq_skip, rvtype="uniform", scale=CONF_coeff_scale, secondparam=muparam)
# setup boundary conditions and pde
# initial_mesh_N = CONF_initial_mesh_N
pde, Dirichlet_boundary, uD, Neumann_boundary, g, f = SampleProblem.setupPDE(CONF_boundary_type, CONF_domain, CONF_problem_type, boundaries, coeff_field)
# define multioperator
A = MultiOperator(coeff_field, pde.assemble_operator, pde.assemble_operator_inner_dofs, assembly_type=eval("ASSEMBLY_TYPE." + CONF_assembly_type))
# ============================================================
# PART B: Import Solution
# ============================================================
import pickle
LOAD_SOLUTION = os.path.join(opts.basedir, CONF_experiment_name)
logger.info("loading solutions from %s" % os.path.join(LOAD_SOLUTION, 'SFEM-SOLUTIONS.pkl'))
# load solutions
with open(os.path.join(LOAD_SOLUTION, 'SFEM-SOLUTIONS.pkl'), 'rb') as fin:
w_history = pickle.load(fin)
# load simulation data
logger.info("loading statistics from %s" % os.path.join(LOAD_SOLUTION, 'SIM-STATS.pkl'))
with open(os.path.join(LOAD_SOLUTION, 'SIM-STATS.pkl'), 'rb') as fin:
sim_stats = pickle.load(fin)
logger.info("active indices of w after initialisation: %s", w_history[-1].active_indices())
# ============================================================
# PART C: MC Error Sampling
# ============================================================
MC_N = CONF_N
MC_HMAX = CONF_max_h
if CONF_runs > 0:
# determine reference mesh
w = w_history[-1]
ref_mesh, _ = create_joint_mesh([w[mu].mesh for mu in w.active_indices()])
for _ in range(CONF_ref_mesh_refine):
ref_mesh = refine(ref_mesh)
ref_maxm = CONF_sampling_order if CONF_sampling_order > 0 else w.max_order + CONF_sampling_order_increase
for i, w in enumerate(w_history):
# if i == 0:
# continue
logger.info("MC error sampling for w[%i] (of %i)", i, len(w_history))
# memory usage info
import resource
logger.info("\n======================================\nMEMORY USED: " + str(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) + "\n======================================\n")
MC_start = 0
old_stats = sim_stats[i]
if opts.continueMC:
try:
MC_start = sim_stats[i]["MC-N"]
logger.info("CONTINUING MC of %s for solution (iteration) %s of %s", LOAD_SOLUTION, i, len(w_history))
except:
logger.info("STARTING MC of %s for solution (iteration) %s of %s", LOAD_SOLUTION, i, len(w_history))
if MC_start <= 0:
sim_stats[i]["MC-N"] = 0
sim_stats[i]["MC-L2ERR"] = 0
sim_stats[i]["MC-H1ERR"] = 0
sim_stats[i]["MC-L2ERR_a0"] = 0
sim_stats[i]["MC-H1ERR_a0"] = 0
MC_RUNS = max(CONF_runs - MC_start, 0)
if MC_RUNS > 0:
logger.info("STARTING %s MC RUNS", MC_RUNS)
# L2err, H1err, L2err_a0, H1err_a0, N = sample_error_mc(w, pde, A, coeff_field, mesh0, ref_maxm, MC_RUNS, MC_N, MC_HMAX)
L2err, H1err, L2err_a0, H1err_a0, N = sample_error_mc(w, pde, A, coeff_field, ref_mesh, ref_maxm, MC_RUNS, MC_N, MC_HMAX)
# combine current and previous results
sim_stats[i]["MC-N"] = N + old_stats["MC-N"]
sim_stats[i]["MC-L2ERR"] = (L2err * N + old_stats["MC-L2ERR"]) / sim_stats[i]["MC-N"]
sim_stats[i]["MC-H1ERR"] = (H1err * N + old_stats["MC-H1ERR"]) / sim_stats[i]["MC-N"]
sim_stats[i]["MC-L2ERR_a0"] = (L2err_a0 * N + old_stats["MC-L2ERR_a0"]) / sim_stats[i]["MC-N"]
sim_stats[i]["MC-H1ERR_a0"] = (H1err_a0 * N + old_stats["MC-H1ERR_a0"]) / sim_stats[i]["MC-N"]
print "MC-H1ERR (N:%i) = %f" % (sim_stats[i]["MC-N"], sim_stats[i]["MC-H1ERR"])
else:
logger.info("SKIPPING MC RUN since sufficiently many samples are available")
# ============================================================
# PART D: Export Updated Data and Plotting
# ============================================================
# save updated data
if opts.saveData:
# save updated statistics
import pickle
SAVE_SOLUTION = os.path.join(opts.basedir, CONF_experiment_name)
try:
os.makedirs(SAVE_SOLUTION)
except:
pass
logger.info("saving statistics into %s" % os.path.join(SAVE_SOLUTION, 'SIM-STATS.pkl'))
with open(os.path.join(SAVE_SOLUTION, 'SIM-STATS.pkl'), 'wb') as fout:
pickle.dump(sim_stats, fout)
# plot residuals
if opts.plotEstimator and len(sim_stats) > 1:
try:
from matplotlib.pyplot import figure, show, legend
x = [s["DOFS"] for s in sim_stats]
L2 = [s["L2"] for s in sim_stats]
H1 = [s["H1"] for s in sim_stats]
errest = [sqrt(s["EST"]) for s in sim_stats]
res_part = [s["RES-PART"] for s in sim_stats]
proj_part = [s["PROJ-PART"] for s in sim_stats]
pcg_part = [s["PCG-PART"] for s in sim_stats]
_reserrmu = [s["RES-mu"] for s in sim_stats]
_projerrmu = [s["PROJ-mu"] for s in sim_stats]
if CONF_runs > 0:
mcL2 = [s["MC-L2ERR"] for s in sim_stats]
mcH1 = [s["MC-H1ERR"] for s in sim_stats]
mcL2_a0 = [s["MC-L2ERR_a0"] for s in sim_stats]
mcH1_a0 = [s["MC-H1ERR_a0"] for s in sim_stats]
effest = [est / err for est, err in zip(errest, mcH1)]
mi = [s["MI"] for s in sim_stats]
num_mi = [len(m) for m in mi]
reserrmu = defaultdict(list)
for rem in _reserrmu:
for mu, v in rem:
reserrmu[mu].append(v)
print "errest", errest
if CONF_runs > 0:
print "mcH1", mcH1
print "efficiency", [est / err for est, err in zip(errest, mcH1)]
# --------
# figure 2
# --------
fig2 = figure()
fig2.suptitle("residual estimator")
ax = fig2.add_subplot(111)
if CONF_refine_Lambda:
ax.loglog(x, num_mi, '--y+', label='active mi')
ax.loglog(x, errest, '-g<', label='error estimator')
ax.loglog(x, res_part, '-.cx', label='residual part')
ax.loglog(x[1:], proj_part[1:], '-.m>', label='projection part')
ax.loglog(x, pcg_part, '-.b>', label='pcg part')
if MC_RUNS > 0:
ax.loglog(x, mcH1, '-b^', label='MC H1 error')
ax.loglog(x, mcL2, '-ro', label='MC L2 error')
# ax.loglog(x, H1, '-b^', label='H1 residual')
# ax.loglog(x, L2, '-ro', label='L2 residual')
legend(loc='upper right')
# --------
# figure 3
# --------
fig3 = figure()
fig3.suptitle("efficiency residual estimator")
ax = fig3.add_subplot(111)
ax.loglog(x, errest, '-g<', label='error estimator')
if MC_RUNS > 0:
ax.loglog(x, mcH1, '-b^', label='MC H1 error')
ax.loglog(x, effest, '-ro', label='efficiency')
legend(loc='upper right')
# # --------
# # figure 4
# # --------
# fig4 = figure()
# fig4.suptitle("residual contributions")
# ax = fig4.add_subplot(111)
# for mu, v in reserrmu.iteritems():
# ms = str(mu)
# ms = ms[ms.find('=') + 1:-1]
# ax.loglog(x[-len(v):], v, '-g<', label=ms)
# legend(loc='upper right')
show() # this invalidates the figure instances...
except:
import traceback
print traceback.format_exc()
logger.info("skipped plotting since matplotlib is not available...")