def test_neg():
mv1 = MultiVector()
mis1 = MultiindexSet.createCompleteOrderSet(3, 4)
mv1.set_defaults(mis1, FlatVector([3, 4, 5]))
mv = -mv1
assert_equal(mv[Multiindex(mis1[-1])], FlatVector([-3, -4, -5]))
assert_equal(mv1[Multiindex(mis1[-1])], FlatVector([3, 4, 5]))
def test_set_defaults():
mv = MultiVector()
mis = MultiindexSet.createCompleteOrderSet(3, 4)
mv.set_defaults(mis, FlatVector([3, 4, 5]))
assert_equal(mv[Multiindex([1, 2, 1])], FlatVector([3, 4, 5]))
assert_equal(mv[Multiindex()], FlatVector([3, 4, 5]))
assert_raises(KeyError, mv.__getitem__, Multiindex([1, 2, 2]))
def test_equality():
mv1 = MultiVector()
mv2 = MultiVector()
mv3 = MultiVector()
mv4 = MultiVector()
mis1 = MultiindexSet.createCompleteOrderSet(3, 4)
mis2 = MultiindexSet.createCompleteOrderSet(3, 5)
mv1.set_defaults(mis1, FlatVector([3, 4, 5]))
mv2.set_defaults(mis1, FlatVector([3, 4, 5]))
mv3.set_defaults(mis2, FlatVector([3, 4, 5]))
mv4.set_defaults(mis1, FlatVector([3, 4, 6]))
assert_true(mv1 == mv2)
assert_false(mv1 != mv2)
assert_true(mv1 != mv3)
assert_false(mv1 == mv3)
assert_true(mv1 != mv4)
assert_false(mv1 == mv4)
def test_add():
mv1 = MultiVector()
mv2 = MultiVector()
mv3 = MultiVector()
mis1 = MultiindexSet.createCompleteOrderSet(3, 4)
mv1.set_defaults(mis1, FlatVector([3, 4, 5]))
mv2.set_defaults(mis1, FlatVector([6, 8, 12]))
mv3.set_defaults(mis1, FlatVector([9, 12, 17]))
assert_equal(mv1 + mv2, mv3)
def prepare_stochastic_operators(M, p1, p2=0, type='L'):
I = MultiindexSet.createCompleteOrderSet(M, p1).arr
if type == 'L':
print "Legendre triple", I.shape
polysys = LegendrePolynomials()
L = evaluate_triples(polysys, I, I)
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 initialise_multivector(mv, M):
# initial multiindices
mis = [Multiindex(mis) for mis in MultiindexSet.createCompleteOrderSet(M, 1)]
# intialise fem vectors
N = 15
mesh = UnitSquareMesh(N, N)
V = FunctionSpace(mesh, 'CG', 1)
ex = Expression('sin(2*pi*A*x[0])', A=0)
for i, mi in enumerate(mis):
ex.A = i+1
f = interpolate(ex, V)
mv[mi] = FEniCSVector(f)
def test_sub():
mv1 = MultiVector()
mv2 = MultiVector()
mi1 = Multiindex([1, 2, 1])
mi2 = Multiindex([3, 2, 1, 7])
mis1 = MultiindexSet.createCompleteOrderSet(3, 4)
mv1.set_defaults(mis1, FlatVector([3, 4, 5]))
mv2.set_defaults(mis1, FlatVector([6, 8, 10]))
mv1[mi2] = FlatVector([7, 10, 6])
mv2[mi2] = FlatVector([2, 6, 13])
mv3 = mv1 - mv2
assert_equal(mv3[mi1], FlatVector([-3, -4, -5]))
assert_equal(mv3[mi2], FlatVector([5, 4, -7]))
def test_mul():
mv1 = MultiVector()
mv2 = MultiVector()
mis1 = MultiindexSet.createCompleteOrderSet(3, 4)
#mis2 = MultiindexSet.createCompleteOrderSet(3, 5)
mv1.set_defaults(mis1, FlatVector([3, 4, 5]))
mv2.set_defaults(mis1, FlatVector([6, 8, 10]))
assert_equal(2 * mv1, mv2)
assert_equal(mv1 * 2, mv2)
assert_equal(2.0 * mv1, mv2)
assert_equal(mv1 * 2.0, mv2)
assert_equal(mv1[Multiindex()], FlatVector([3, 4, 5]))
assert_equal(mv1[Multiindex([1, 2, 1])], FlatVector([3, 4, 5]))
mv1 *= 2.0
assert_equal(mv1, mv2)
def setupCF2(cls, functype, amptype, rvtype='uniform', gamma=0.9, decayexp=2, freqscale=1, freqskip=0, N=1, scale=1, dim=2, secondparam=None):
try:
rvs = cls.rv_defs[rvtype]
except KeyError:
raise ValueError("Unknown RV type %s", rvtype)
try:
func = cls.func_defs[(functype, dim)]
except KeyError:
raise ValueError("Unknown function type %s for dim %s", functype, dim)
if amptype == "decay-inf":
start = SampleProblem.get_decay_start(decayexp, gamma)
amp = gamma / zeta(decayexp, start)
ampfunc = lambda i: amp / (float(i) + start) ** decayexp
logger.info("type is decay_inf with start = " + str(start) + " and amp = " + str(amp))
elif amptype == "constant":
amp = gamma / N
ampfunc = lambda i: gamma * (i < N)
else:
raise ValueError("Unknown amplitude type %s", amptype)
logger.info("amp function: %s", str([ampfunc(i) for i in range(10)]))
element = FiniteElement('Lagrange', ufl.triangle, 1)
# NOTE: the explicit degree of the expression should influence the quadrature order during assembly
degree = 3
mis = MultiindexSet.createCompleteOrderSet(dim)
for i in range(freqskip + 1):
mis.next()
a0 = Expression("B", element=element, B=scale)
if dim == 1:
a = (Expression(func, freq=freqscale, A=ampfunc(i), B=scale,
m=int(mu[0]), degree=degree, element=element) for i, mu in enumerate(mis))
else:
a = (Expression(func, freq=freqscale, A=ampfunc(i), B=scale,
m=int(mu[0]), n=int(mu[1]),
degree=degree, element=element) for i, mu in enumerate(mis))
if secondparam is not None:
from itertools import izip
a0 = (a0, secondparam[0])
a = ((am, bm) for am, bm in izip(a, secondparam[1]))
return ParametricCoefficientField(a0, a, rvs)
def test_mvwp_copy():
# compares equal to copied MultiVectorWP but not to MultiVector
mv0 = MultiVector()
mv1 = MultiVectorWithProjection()
mis1 = MultiindexSet.createCompleteOrderSet(3, 4)
mv0.set_defaults(mis1, FlatVector([3, 4, 5]))
mv1.set_defaults(mis1, FlatVector([3, 4, 5]))
mv2 = mv1.copy()
assert_equal(mv2, mv1)
assert_not_equal(mv2, mv0)
# compares equal if project methods match, make sure project method is copied
mv3 = MultiVectorWithProjection(project=lambda : None)
mv3.set_defaults(mis1, FlatVector([3, 4, 5]))
mv4 = mv3.copy()
assert_not_equal(mv2, mv3)
assert_equal(mv4, mv3)
# initial mesh elements
initial_mesh_N = CONF_initial_mesh_N
# plotting flag
PLOT_SOLUTION = True
# 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)
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()
from matplotlib.pyplot import figure, show, spy
from spuq.math_utils.multiindex_set import MultiindexSet
from spuq.polyquad.structure_coefficients import evaluate_triples
from spuq.polyquad.polynomials import LegendrePolynomials
I = MultiindexSet.createCompleteOrderSet(4, 3, reversed=True).arr
print I
#H = evaluate_Hermite_triple(I, I, J)
#print "shape of H:", H.shape
# create polynomial instance
lp = LegendrePolynomials()
L = evaluate_triples(lp, I, I)
print len(L), L[0].shape
# fig = figure()
# spy(np.sum(H, axis=2))
fig = figure()
#spy(np.sum(L))
spy(L[3])
show()
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()
from spuq.fem.fenics.fenics_basis import FEniCSBasis from spuq.math_utils.multiindex_set import MultiindexSet from spuq.math_utils.multiindex import Multiindex from dolfin import UnitSquareMesh, FunctionSpace import numpy as np # setup covariance GCV = GaussianCovariance(sigma=1, a=1) # construct discrete function space N = 3 mesh = UnitSquareMesh(N, N) V = FunctionSpace(mesh, 'CG', 1) basis = FEniCSBasis(V) # evaluate KL expansion KL = KLexpansion(GCV, basis, M=5) # evaluate transformed covariance # initial multiindices mis = [Multiindex(mis) for mis in MultiindexSet.createCompleteOrderSet(3, 1)] sigma_, mu_ = 1, 0 phi = lambda gamma: np.exp(sigma_*gamma + mu_) TCV = TransformedCovariance(mis, phi, KL, N=3) # evaluate KL of transfor KL2 = KLexpansion(TCV, basis, M=5) # get pce coefficients of KL r = eval_pce_from_KL(mis, KL, TCV._phii)
def test_init(self):
I = MultiindexSet.createCompleteOrderSet(2, 4)
def setupCF2(cls, functype, amptype, rvtype='uniform', gamma=0.9, decayexp=2, freqscale=1, freqskip=0, N=1, scale=1, dim=2, secondparam=None):
try:
rvs = cls.rv_defs[rvtype]
except KeyError:
raise ValueError("Unknown RV type %s", rvtype)
try:
func = cls.func_defs[(functype, dim)]
except KeyError:
raise ValueError("Unknown function type %s for dim %s", functype, dim)
if amptype == "decay-inf":
start = SampleProblem.get_decay_start(decayexp, gamma)
amp = gamma / zeta(decayexp, start)
ampfunc = lambda i: amp / (float(i) + start) ** decayexp
logger.info("type is decay_inf with start = " + str(start) + " and amp = " + str(amp))
elif amptype == "constant":
amp = gamma / N
ampfunc = lambda i: gamma * (i < N)
else:
raise ValueError("Unknown amplitude type %s", amptype)
logger.info("amp function: %s", str([ampfunc(i) for i in range(10)]))
element = FiniteElement('Lagrange', ufl.triangle, 1)
# NOTE: the explicit degree of the expression should influence the quadrature order during assembly
# TODO: this needs some serious thoughts!
degree = 3
mis = MultiindexSet.createCompleteOrderSet(dim)
for i in range(freqskip + 1):
mis.next()
def generate_expression(func, freq, A, B, m, n, degree, element):
func, min_val, max_val, max_grad = func
if n is None:
ex = Expression(func, freq=freq, A=A, B=B,
m=m, degree=degree, element=element)
else:
ex = Expression(func, freq=freqscale, A=A, B=B,
m=m, n=n, degree=degree, element=element)
try:
for k, v in {"freq":freq, "A":A, "B":B, "m":m, "n":n, "pi":"np.pi"}.iteritems():
v = str(v)
min_val = min_val.replace(k, v)
max_val = max_val.replace(k, v)
max_grad = max_grad.replace(k, v)
ex.min_val = eval(min_val)
ex.max_val = eval(max_val)
ex.max_grad = eval(max_grad)
except:
logger.info("no min/max info available for coefficients")
return ex
a0 = generate_expression(("B", "B", "B", "1.0"), freq=freqscale, A=1, B=scale, m=0, n=None, degree=0, element=element)
if dim == 1:
a = (generate_expression(func=func, freq=freqscale, A=ampfunc(i), B=scale,
m=int(mu[0]), n=None, degree=degree, element=element) for i, mu in enumerate(mis))
else:
a = (generate_expression(func=func, freq=freqscale, A=ampfunc(i), B=scale,
m=int(mu[0]), n=int(mu[1]), degree=degree, element=element) for i, mu in enumerate(mis))
if secondparam is not None:
from itertools import izip
a0 = (a0, secondparam[0])
a = ((am, bm) for am, bm in izip(a, secondparam[1]))
return ParametricCoefficientField(a0, a, rvs)
