from spuq.utils.multiindex_set import *
I = MultiindexSet.createCompleteOrderSet(2, 4)
print I
from spuq.statistics import *
N = NormalDistribution()
U = UniformDistribution()
print N, U
gpc1 = GPCBasis(I, [N, U])
gpc2 = GPCBasis(I, [N, N])
print gpc1.sample(3)
s1 = gpc1.sample(100)
s2 = gpc2.sample(100)
from spuq.utils.plot.plotter import Plotter
Plotter.figure(1)
Plotter.scatterplot(I.arr[:7, :], s1)
Plotter.figure(2)
Plotter.scatterplot(I.arr[8:15, :], s2)
Plotter.figure(3)
Plotter.histplot(s1[:6, :], bins=50)
# multiplication tensor: first as numpy array 3d
# then:
# class MultiplicationTensor
# def contract( vector ) -> (sparse) matrix
# def contract( vector, vector ) -> vector
# storage: full, sparse matrix, own sparse format?
class MultiplicationTensor:
mu, lmbda = E/(2.0*(1.0 + nu)), E*nu/((1.0 + nu)*(1.0 - 2.0*nu))
# Stress
sigma = 2*mu*sym(grad(u)) + lmbda*tr(grad(u))*Identity(w.cell().d)
# Governing balance equation
F = inner(sigma, grad(w))*dx - dot(b, w)*dx
# Extract bilinear and linear forms from F
a, L = lhs(F), rhs(F)
# Dirichlet boundary condition on entire boundary
def uD_boundary1(x, on_boundary):
return abs(x[0]) <= 0 and on_boundary
def uD_boundary2(x, on_boundary):
return abs(x[0]) >= 1 and on_boundary
bc1 = DirichletBC(V, Constant((0,0)), uD_boundary1)
bc2 = DirichletBC(V, Constant((0,0.3)), uD_boundary2)
# Set up PDE and solve
u = Function(V)
problem = LinearVariationalProblem(a, L, u, bcs=[bc1,bc2])
solver = LinearVariationalSolver(problem)
solver.parameters["symmetric"] = True
solver.solve()
if not MAYAVI_PLOTTING:
plot(u,mode="displacement",interactive=True,wireframe=True)
else:
Plotter.plotMesh(u,displacement=True)
Plotter.show()
# # 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), axes=True)
## plot(wi[mu]._fefunc.function_space().mesh(), title="parametric solution " + str(mu) + " iteration " + str(i), axes=True)
# interactive()
# # ---debug
mesh_param = sample_sol_param._fefunc.function_space().mesh()
mesh_direct = sample_sol_direct._fefunc.function_space().mesh()
wireframe = True
if not MAYAVI_PLOTTING:
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)
else:
PLOTSCALE = 30 if CONF_boundary_type == 3 else 1
Plotter.plotMesh(sample_sol_param._fefunc, displacement=True, scale=PLOTSCALE)
Plotter.plotMesh(sample_sol_direct._fefunc, displacement=True, scale=PLOTSCALE)
for mu in w.active_indices():
if not MAYAVI_PLOTTING:
viz_p = plot(w[mu]._fefunc, title="parametric solution: " + str(mu), mode="displacement", mesh=mesh_param, wireframe=wireframe)
else:
Plotter.plotMesh(w[mu]._fefunc, displacement=True, scale=PLOTSCALE)
if not MAYAVI_PLOTTING:
interactive()
else:
Plotter.show()
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()
sol_variance = compute_solution_variance(coeff_field, w, projection_basis)
# # 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), axes=True)
## plot(wi[mu]._fefunc.function_space().mesh(), title="parametric solution " + str(mu) + " iteration " + str(i), axes=True)
# interactive()
# # ---debug
mesh_param = sample_sol_param._fefunc.function_space().mesh()
mesh_direct = sample_sol_direct._fefunc.function_space().mesh()
wireframe = True
if not MAYAVI_PLOTTING:
viz_p = plot(sample_sol_param._fefunc, title="parametric solution", wireframe=wireframe)#, rescale=False)
viz_d = plot(sample_sol_direct._fefunc, title="direct solution", wireframe=wireframe)#, rescale=False)
else:
Plotter.plotMesh(sample_sol_param._fefunc)
Plotter.plotMesh(sample_sol_direct._fefunc)
for mu in w.active_indices():
if not MAYAVI_PLOTTING:
viz_p = plot(w[mu]._fefunc, title="parametric solution: " + str(mu), mode="displacement", mesh=mesh_param, wireframe=wireframe)
else:
Plotter.plotMesh(w[mu]._fefunc)
if not MAYAVI_PLOTTING:
interactive()
else:
Plotter.show()
ms = ms[ms.find('=') + 1:-1]
ax.loglog(x[-len(v):], v, '-g<', label=ms)
legend(loc='upper right')
# if SAVE_SOLUTION != "":
# fig4.savefig(os.path.join(SAVE_SOLUTION, 'RESCONTRIB.png'))
# fig4.savefig(os.path.join(SAVE_SOLUTION, 'RESCONTRIB.eps'))
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 PLOT_MESHES:
USE_MAYAVI = Plotter.hasMayavi() and False
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()
# # ---debug
mesh_param = sample_sol_param._fefunc.function_space().mesh()
mesh_direct = sample_sol_direct._fefunc.function_space().mesh()
V=sample_sol_param._fefunc.function_space()
Vd = VectorFunctionSpace(V.mesh(), "DG", 0)
gradsol=project(grad(sample_sol_param._fefunc),Vd)
gradsolx, gradsoly=gradsol.split(deepcopy=True)
#grad_y = project(dolfin.inner(grad(sample_sol_param._fefunc),Constant((1.0,0.0))), V)
MAYAVI_PLOTTING = False
if not MAYAVI_PLOTTING:
wireframe = not True
viz_p = plot(sample_sol_param._fefunc, title="parametric solution", mesh=mesh_param, wireframe=wireframe)#, rescale=False)
viz_d = plot(sample_sol_direct._fefunc, title="direct solution", mesh=mesh_direct, wireframe=wireframe)#, rescale=False)
viz_x = plot(gradsolx, title="x-gradient solution", wireframe=wireframe)#, rescale=False)
viz_y = plot(gradsoly, title="y-gradient solution", wireframe=wireframe)#, rescale=False)
else:
Plotter.plotMesh(sample_sol_param._fefunc)
Plotter.plotMesh(sample_sol_direct._fefunc)
Plotter.plotMesh(gradsolx)
Plotter.plotMesh(gradsoly)
if not MAYAVI_PLOTTING:
interactive()
else:
Plotter.show()
from dolfin import Function, UnitSquare, FunctionSpace, VectorFunctionSpace, Expression
from spuq.utils.plot.plotter import Plotter
N = 30
mesh = UnitSquare(N,N)
V = FunctionSpace(mesh,'CG',1)
f = Function(V)
ex = Expression("x[0]*x[1]")
f.interpolate(ex)
Plotter.figure()
Plotter.plotMesh(f)
Plotter.axes()
Plotter.show()
VV = VectorFunctionSpace(mesh,'CG',1)
ff = Function(VV)
exx = Expression(["x[0]*x[1]/10.","sin(2*pi*x[0])/10."])
ff.interpolate(exx)
Plotter.figure()
Plotter.plotMesh(ff, displacement=True)
Plotter.axes()
Plotter.show()