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)
print "K", len(K)
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
_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()
