def __init__(self, name='mesh', filename=None,
prefix_dir=None, **kwargs):
"""Create a Mesh.
Parameters
----------
name : str
Object name.
filename : str
Loads a mesh from the specified file, if not None.
prefix_dir : str
If not None, the filename is relative to that directory.
"""
Struct.__init__(self, name=name, **kwargs)
self.nodal_bcs = {}
if filename is None:
self.io = None
self.setup_done = 0
else:
io = MeshIO.any_from_filename(filename, prefix_dir=prefix_dir)
output('reading mesh (%s)...' % (io.filename))
tt = time.clock()
io.read(self)
output('...done in %.2f s' % (time.clock() - tt))
self._set_shape_info()
def conv_test( conf, it, of, of0, ofg_norm = None ):
"""
Returns
-------
flag : int
* -1 ... continue
* 0 ... small OF -> stop
* 1 ... i_max reached -> stop
* 2 ... small OFG -> stop
* 3 ... small relative decrase of OF
"""
status = -1
output( 'opt: iter: %d, of: %e (||ofg||: %e)' % (it, of, ofg_norm) )
# print (of0 - of), (conf.eps_rd * of0)
if (abs( of ) < conf.eps_of):
status = 0
elif ofg_norm and (ofg_norm < conf.eps_ofg):
status = 2
elif (it > 0) and (abs(of0 - of) < (conf.eps_rd * abs( of0 ))):
status = 3
if (status == -1) and (it >= conf.i_max):
status = 1
return status
def setup_dof_conns(conn_info, dof_conns=None,
make_virtual=False, verbose=True):
"""
Dof connectivity key:
(field.name, var.n_components, region.name, type, ig)
"""
if verbose:
output('setting up dof connectivities...')
tt = time.clock()
dof_conns = get_default(dof_conns, {})
for key, ii, info in iter_dict_of_lists(conn_info, return_keys=True):
if info.primary is not None:
var = info.primary
field = var.get_field()
field.setup_extra_data(info.ps_tg, info, info.is_trace)
field.setup_dof_conns(dof_conns, var.n_components,
info.dc_type, info.get_region(),
info.is_trace)
if info.has_virtual and not info.is_trace:
# This is needed regardless make_virtual.
var = info.virtual
field = var.get_field()
field.setup_extra_data(info.v_tg, info, False)
field.setup_dof_conns(dof_conns, var.n_components,
info.dc_type,
info.get_region(can_trace=False))
if verbose:
output('...done in %.2f s' % (time.clock() - tt))
return dof_conns
def __call__(self, vec0=None, nls=None, init_fun=None, prestep_fun=None,
poststep_fun=None, status=None, **kwargs):
"""
Solve elastodynamics problems by the Newmark method.
"""
conf = self.conf
nls = get_default(nls, self.nls)
vec, unpack, pack = self.get_initial_vec(
nls, vec0, init_fun, prestep_fun, poststep_fun)
ts = self.ts
for step, time in ts.iter_from(ts.step):
output(self.format % (time, step + 1, ts.n_step),
verbose=self.verbose)
dt = ts.dt
prestep_fun(ts, vec)
ut, vt, at = unpack(vec)
nlst = self.create_nlst(nls, dt, conf.gamma, conf.beta, ut, vt, at)
atp = nlst(at)
vtp = nlst.v(atp)
utp = nlst.u(atp)
vect = pack(utp, vtp, atp)
poststep_fun(ts, vect)
vec = vect
return vec
def make_explicit_step(ts, state0, problem, mass, nls_status=None):
problem.time_update(ts)
if ts.step == 0:
state0.apply_ebc()
state = state0.copy(deep=True)
problem.init_time(ts)
# Initialize variables with history.
state0.init_history()
ev = problem.get_evaluator()
try:
vec_r = ev.eval_residual(state0(), is_full=True)
except ValueError:
output('residual evaluation failed, giving up...')
raise
else:
err = nm.linalg.norm(vec_r)
output('residual: %e' % err)
if ts.step > 0:
variables = problem.get_variables()
vec_rf = variables.make_full_vec(vec_r, force_value=0.0)
rhs = -ts.dt * vec_rf + mass.action(state0())
vec = mass.inverse_action(rhs)
state = state0.copy(preserve_caches=True)
state.set_full(vec)
state.apply_ebc()
return state
def triangulate(mesh, verbose=False):
"""
Triangulate a 2D or 3D tensor product mesh: quadrilaterals->triangles,
hexahedrons->tetrahedrons.
Parameters
----------
mesh : Mesh
The input mesh.
Returns
-------
mesh : Mesh
The triangulated mesh.
"""
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo, verbose=verbose)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
output('new mesh: %d elements' % new_conns.shape[0], verbose=verbose)
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])
return mesh
def get_conductivity(ts, coors, problem, equations = None, mode = None, **kwargs):
"""
Calculates the conductivity with a constitutive k(psi) relation,
where psi = -h.
"""
if mode == 'qp':
## Get pressure values
h_values = problem.evaluate('ev_volume_integrate.i.Omega(h)',
mode = 'qp', verbose = False) * scaling
psi_values = -h_values
# van Genuchten
val = vanGenuchten(ksat = silt_ksat, aVG = silt_aVG, nVG = silt_nVG,
mVG = silt_mVG, lVG = silt_lVG, psi = psi_values)
# Brooks and Corey
#val = brooksCorey(ksat = silt_ksat, aev = silt_aev, lBC = silt_lBC,
# psi = psi_values)
# Reshape the val vector to match SfePy expectations
val.shape = (val.shape[0] * val.shape[1], 1, 1)
# Check output
output('h_values: min:', h_values.min(), 'max:', h_values.max())
output('conductivity: min:', val.min(), 'max:', val.max())
return {'val' : val}
def igs(self):
"""
Cell group indices according to region kind.
"""
if self.parent is not None:
self._igs = self.domain.regions[self.parent].igs
elif self._igs is None:
if 'vertex' in self.true_kind:
self._igs = self.domain.cmesh.get_igs(self.vertices, 0)
elif 'edge' in self.true_kind:
self._igs = self.domain.cmesh.get_igs(self.edges, 1)
elif 'face' in self.true_kind:
self._igs = self.domain.cmesh.get_igs(self.faces, 2)
elif 'cell' in self.true_kind:
self._igs = self.domain.cmesh.get_igs(self.cells, self.tdim)
if not len(self._igs):
output('warning: region %s of %s kind has empty group indices!'
% (self.name, self.kind))
return self._igs
def create_conn_graph(self, verbose=True):
"""
Create a graph of mesh connectivity.
Returns
-------
graph : csr_matrix
The mesh connectivity graph as a SciPy CSR matrix.
"""
from extmods.cmesh import create_mesh_graph
shape = (self.n_nod, self.n_nod)
output('graph shape:', shape, verbose=verbose)
if nm.prod(shape) == 0:
output('no graph (zero size)!', verbose=verbose)
return None
output('assembling mesh graph...', verbose=verbose)
tt = time.clock()
nnz, prow, icol = create_mesh_graph(shape[0], shape[1],
len(self.conns),
self.conns, self.conns)
output('...done in %.2f s' % (time.clock() - tt), verbose=verbose)
output('graph nonzeros: %d (%.2e%% fill)' \
% (nnz, float(nnz) / nm.prod(shape)))
data = nm.ones((nnz,), dtype=nm.bool)
graph = sp.csr_matrix((data, icol, prow), shape)
return graph
def setup_facets(self, create_edges=True, create_faces=True,
verbose=False):
"""
Setup the edges and faces (in 3D) of domain elements.
"""
kinds = ['edges', 'faces']
is_face = self.has_faces()
create = [create_edges, create_faces and is_face]
for ii, kind in enumerate(kinds):
if create[ii]:
if verbose:
output('setting up domain %s...' % kind)
tt = time.clock()
obj = Facets.from_domain(self, kind)
obj.sort_and_orient()
obj.setup_unique()
obj.setup_neighbours()
# 'ed' or 'fa'
setattr(self, kind[:2], obj)
if verbose:
output('...done in %.2f s' % (time.clock() - tt))
if not is_face:
self.fa = None
def __call__( self, problem = None, data = None, save_hook = None ):
"""data: corrs_pressure, evp, optionally vec_g"""
problem = get_default( problem, self.problem )
ts = problem.get_time_solver().ts
corrs, evp = [data[ii] for ii in self.requires[:2]]
if len(self.requires) == 3:
vec_g = data[self.requires[2]]
else:
vec_g = None
assert_( evp.ebcs == self.ebcs )
assert_( evp.epbcs == self.epbcs )
filename = self.get_dump_name()
savename = self.get_save_name()
self.setup_equations(self.equations)
solve = self.compute_correctors
solve(evp, 1.0, corrs.state, ts, filename, savename, vec_g=vec_g)
if self.check:
self.setup_equations(self.verify_equations)
self.init_solvers(problem)
output( 'verifying correctors %s...' % self.name )
verify = self.verify_correctors
ok = verify(1.0, corrs.state, filename)
output( '...done, ok: %s' % ok )
return Struct( name = self.name,
filename = filename )
def main():
from sfepy.base.base import output
from sfepy.base.conf import ProblemConf, get_standard_keywords
from sfepy.discrete import Problem
output.prefix = "therel:"
required, other = get_standard_keywords()
conf = ProblemConf.from_file(__file__, required, other)
problem = Problem.from_conf(conf, init_equations=False)
# Setup output directory according to options above.
problem.setup_default_output()
# First solve the stationary electric conduction problem.
problem.set_equations({"eq": conf.equations["1"]})
problem.time_update()
state_el = problem.solve()
problem.save_state(problem.get_output_name(suffix="el"), state_el)
# Then solve the evolutionary heat conduction problem, using state_el.
problem.set_equations({"eq": conf.equations["2"]})
phi_var = problem.get_variables()["phi_known"]
phi_var.set_data(state_el())
time_solver = problem.get_time_solver()
time_solver()
output("results saved in %s" % problem.get_output_name(suffix="*"))
def refine_mesh(filename, level):
"""
Uniformly refine `level`-times a mesh given by `filename`.
The refined mesh is saved to a file with name constructed from base
name of `filename` and `level`-times appended `'_r'` suffix.
Parameters
----------
filename : str
The mesh file name.
level : int
The refinement level.
"""
import os
from sfepy.base.base import output
from sfepy.fem import Mesh, Domain
if level > 0:
mesh = Mesh.from_file(filename)
domain = Domain(mesh.name, mesh)
for ii in range(level):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
suffix = os.path.splitext(filename)[1]
filename = domain.name + suffix
domain.mesh.write(filename, io='auto')
return filename
def post_process(out, pb, state, extend=False):
"""
Calculate :math:`\nabla t` and compute boundary fluxes.
"""
dv = pb.evaluate('ev_diffusion_velocity.i.Omega(m.K, t)', mode='el_avg',
verbose=False)
out['dv'] = Struct(name='output_data', mode='cell',
data=dv, dofs=None)
totals = nm.zeros(3)
for gamma in ['Gamma_N', 'Gamma_N0', 'Gamma_D']:
flux = pb.evaluate('d_surface_flux.i.%s(m.K, t)' % gamma,
verbose=False)
area = pb.evaluate('d_surface.i.%s(t)' % gamma, verbose=False)
flux_data = (gamma, flux, area, flux / area)
totals += flux_data[1:]
output('%8s flux: % 8.3f length: % 8.3f flux/length: % 8.3f'
% flux_data)
totals[2] = totals[0] / totals[1]
output(' total flux: % 8.3f length: % 8.3f flux/length: % 8.3f'
% tuple(totals))
return out
def __call__(self, mtx_a, mtx_b=None, n_eigs=None,
eigenvectors=None, status=None, conf=None):
from pysparse import jdsym, itsolvers, precon
output("loading...")
A = self._convert_mat(mtx_a)
output("...done")
if mtx_b is not None:
M = self._convert_mat(mtx_b)
output("solving...")
Atau=A.copy()
Atau.shift(-conf.tau,M)
K=precon.jacobi(Atau)
A=A.to_sss();
if mtx_b is not None:
M=M.to_sss();
method = getattr(itsolvers, conf.method)
kconv, lmbd, Q, it, it_in = jdsym.jdsym(A, M, K, n_eigs, conf.tau,
conf.eps_a, conf.i_max,
method,
clvl=conf.verbosity,
strategy=conf.strategy)
output("number of converged eigenvalues:", kconv)
output("...done")
if status is not None:
status['q'] = Q
status['it'] = it
status['it_in'] = it_in
return lmbd, Q
def get_actual_order(self, geometry):
"""
Return the actual integration order for given geometry.
Parameters
----------
geometry : str
The geometry key describing the integration domain,
see the keys of `sfepy.fem.quadratures.quadrature_tables`.
Returns
-------
order : int
If `self.order` is in quadrature tables it is this
value. Otherwise it is the closest higher order. If no
higher order is available, a warning is printed and the
highest available order is used.
"""
table = quadrature_tables[geometry]
if self.order in table:
order = self.order
else:
orders = table.keys()
ii = nm.searchsorted(orders, self.order)
if ii >= len(orders):
order = max(orders)
output(self._msg1 % (self.order, geometry))
output(self._msg2 % order)
else:
order = orders[ii]
return order
def __call__(self, rhs, x0=None, conf=None, eps_a=None, eps_r=None,
i_max=None, mtx=None, status=None, **kwargs):
eps_a = get_default(eps_a, self.conf.eps_a)
eps_r = get_default(eps_r, self.conf.eps_r)
i_max = get_default(i_max, self.conf.i_max)
eps_d = self.conf.eps_d
# There is no use in caching matrix in the solver - always set as new.
pmtx, psol, prhs = self.set_matrix(mtx)
ksp = self.ksp
ksp.setOperators(pmtx)
ksp.setFromOptions() # PETSc.Options() not used yet...
ksp.setTolerances(atol=eps_a, rtol=eps_r, divtol=eps_d, max_it=i_max)
# Set PETSc rhs, solve, get solution from PETSc solution.
if x0 is not None:
psol[...] = x0
ksp.setInitialGuessNonzero(True)
prhs[...] = rhs
ksp.solve(prhs, psol)
sol = psol[...].copy()
output('%s(%s) convergence: %s (%s)'
% (self.conf.method, self.conf.precond,
ksp.reason, self.converged_reasons[ksp.reason]))
return sol
def __call__(self, state0=None, save_results=True, step_hook=None,
post_process_hook=None, nls_status=None):
"""
Solve the time-dependent problem.
"""
problem = self.problem
ts = self.ts
if state0 is None:
state0 = get_initial_state(problem)
ii = 0
for step, time in ts:
output(self.format % (time, ts.dt, self.adt.wait,
step + 1, ts.n_step))
state = self.solve_step(ts, state0, nls_status=nls_status)
state0 = state.copy(deep=True)
if step_hook is not None:
step_hook(problem, ts, state)
if save_results:
filename = problem.get_output_name(suffix=ts.suffix % ts.step)
problem.save_state(filename, state,
post_process_hook=post_process_hook,
file_per_var=None,
ts=ts)
ii += 1
problem.advance(ts)
return state
def make_implicit_step(ts, state0, problem, nls_status=None):
"""
Make a step of an implicit time stepping solver.
"""
if ts.step == 0:
state0.apply_ebc()
state = state0.copy(deep=True)
if not ts.is_quasistatic:
ev = problem.get_evaluator()
try:
vec_r = ev.eval_residual(state(), is_full=True)
except ValueError:
output('initial residual evaluation failed, giving up...')
raise
else:
err = nm.linalg.norm(vec_r)
output('initial residual: %e' % err)
if problem.is_linear():
mtx = prepare_matrix(problem, state)
problem.try_presolve(mtx)
# Initialize variables with history.
state0.init_history()
if ts.is_quasistatic:
# Ordinary solve.
state = problem.solve(state0=state0, nls_status=nls_status)
else:
problem.time_update(ts)
state = problem.solve(state0=state0, nls_status=nls_status)
return state
def vary_omega1_size( problem ):
"""Vary size of \Omega1. Saves also the regions into options['output_dir'].
Input:
problem: ProblemDefinition instance
Return:
a generator object:
1. creates new (modified) problem
2. yields the new (modified) problem and output container
3. use the output container for some logging
4. yields None (to signal next iteration to Application)
"""
from sfepy.fem import ProblemDefinition
from sfepy.solvers.ts import get_print_info
output.prefix = 'vary_omega1_size:'
diameters = nm.linspace( 0.1, 0.6, 7 ) + 0.001
ofn_trunk, output_format = problem.ofn_trunk, problem.output_format
output_dir = problem.output_dir
join = os.path.join
conf = problem.conf
cf = conf.get_raw( 'functions' )
n_digit, aux, d_format = get_print_info( len( diameters ) + 1 )
for ii, diameter in enumerate( diameters ):
output( 'iteration %d: diameter %3.2f' % (ii, diameter) )
cf['select_circ'] = (lambda coors, domain=None:
select_circ(coors[:,0], coors[:,1], 0, diameter),)
conf.edit('functions', cf)
problem = ProblemDefinition.from_conf( conf )
problem.save_regions( join( output_dir, ('regions_' + d_format) % ii ),
['Omega_1'] )
region = problem.domain.regions['Omega_1']
if not region.has_cells_if_can():
print region
raise ValueError( 'region %s has no cells!' % region.name )
ofn_trunk = ofn_trunk + '_' + (d_format % ii)
problem.setup_output(output_filename_trunk=ofn_trunk,
output_dir=output_dir,
output_format=output_format)
out = []
yield problem, out
out_problem, state = out[-1]
filename = join( output_dir,
('log_%s.txt' % d_format) % ii )
fd = open( filename, 'w' )
log_item = '$r(\Omega_1)$: %f\n' % diameter
fd.write( log_item )
fd.write( 'solution:\n' )
nm.savetxt(fd, state())
fd.close()
yield None
def postprocess(filename_input, filename_results, options):
"""
Postprocess probe data files - replot, integrate data.
"""
from matplotlib import pyplot as plt
header, results = read_results(filename_input,
only_names=options.only_names)
output(header)
fig = plt.figure()
for name, result in results.iteritems():
pars, vals = result[:, 0], result[:, 1]
ii = nm.where(nm.isfinite(vals))[0]
# Nans only at the edges.
assert_(nm.diff(ii).sum() == (len(ii)-1))
val = integrate_along_line(pars[ii], vals[ii], options.radial)
label = r'%s: $\int\ %s' % (name, name)
if options.radial:
label += ' (r)'
label += '$ = %.5e'% val
plt.plot(pars, vals, label=label, lw=0.2, marker='+', ms=1)
plt.ylabel('probed data')
plt.xlabel('probe coordinate')
output(label)
plt.legend()
fig.savefig(filename_results)
def get_homog_mat(ts, coors, mode, term=None, problem=None, **kwargs):
if problem.update_materials_flag == 2 and mode == 'qp':
out = hyperelastic_data['homog_mat']
return {k: nm.array(v) for k, v in six.iteritems(out)}
elif problem.update_materials_flag == 0 or not mode == 'qp':
return
output('get_homog_mat')
dim = problem.domain.mesh.dim
update_var = problem.conf.options.mesh_update_variables[0]
state_u = problem.equations.variables[update_var]
state_u.field.clear_mappings()
family_data = problem.family_data(state_u, term.region,
term.integral, term.integration)
mtx_f = family_data.mtx_f.reshape((coors.shape[0],)
+ family_data.mtx_f.shape[-2:])
out = get_homog_coefs_nonlinear(ts, coors, mode, mtx_f,
term=term, problem=problem,
iteration=problem.iiter, **kwargs)
out['E'] = 0.5 * (la.dot_sequences(mtx_f, mtx_f, 'ATB') - nm.eye(dim))
hyperelastic_data['time'] = ts.step
hyperelastic_data['homog_mat_shape'] = family_data.det_f.shape[:2]
hyperelastic_data['homog_mat'] = \
{k: nm.array(v) for k, v in six.iteritems(out)}
return out
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def _check_region(self, region):
"""
Check whether the `region` can be used for the
field. Non-surface fields require the region to span whole
element groups.
Returns
-------
ok : bool
True if the region is usable for the field.
"""
ok = True
domain = region.domain
for ig in region.igs:
if domain.groups[ig].gel.dim != domain.shape.tdim:
output('cells with a bad topological dimension! (%d == %d)'
% (domain.groups[ig].gel.dim, domain.shape.tdim))
ok = False
break
shape = domain.groups[ig].shape
if region.shape[ig].n_vertex < shape.n_vertex:
output('region does not span a whole element group!')
ok = False
break
return ok
def main():
parser = ArgumentParser(description=__doc__)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('--eps', action='store', dest='eps',
default=1e-12, help=helps['eps'])
parser.add_argument('-o', '--filename-out',
action='store', dest='filename_out',
default=None, help=helps['filename-out'])
parser.add_argument('filename')
options = parser.parse_args()
filename = options.filename
mesh = Mesh.from_file(filename)
mesh_out = extract_edges(mesh, eps=float(options.eps))
mesh_out = merge_lines(mesh_out)
filename_out = options.filename_out
if filename_out is None:
filename_out = edit_filename(filename, prefix='edge_', new_ext='.vtk')
output('Outline mesh - vertices: %d, edges: %d, output filename: %s'
% (mesh_out[0].shape[0], mesh_out[2][0].shape[0], filename_out))
# hack to write '3_2' elements - edges
io = VTKMeshIO(None)
aux_mesh = Struct()
aux_mesh._get_io_data = lambda: mesh_out
aux_mesh.n_el = mesh_out[2][0].shape[0]
io.write(filename_out, aux_mesh)
def create_petsc_system(mtx, sizes, pdofs, drange, is_overlap=True,
comm=None, verbose=False):
"""
Create and pre-allocate (if `is_overlap` is True) a PETSc matrix and
related solution and right-hand side vectors.
"""
if comm is None:
comm = PETSc.COMM_WORLD
if is_overlap:
mtx.data[:] = 1
mtx_prealloc = create_prealloc_data(mtx, pdofs, drange,
verbose=True)
pmtx = create_petsc_matrix(sizes, mtx_prealloc, comm=comm)
else:
pmtx = create_petsc_matrix(sizes, comm=comm)
own_range = pmtx.getOwnershipRange()
output('pmtx ownership:', own_range, verbose=verbose)
assert_(own_range == drange)
psol, prhs = pmtx.getVecs()
own_range = prhs.getOwnershipRange()
output('prhs ownership:', own_range, verbose=verbose)
assert_(own_range == drange)
return pmtx, psol, prhs
def get_dofs_in_region(self, region, merge=False, clean=False, warn=False, igs=None):
"""
Return indices of DOFs that belong to the given region.
"""
if igs is None:
igs = region.igs
nods = []
for ig in self.igs:
if not ig in igs:
nods.append(None)
continue
nn = self.get_dofs_in_region_group(region, ig)
nods.append(nn)
if merge:
nods = [nn for nn in nods if nn is not None]
nods = nm.unique(nm.hstack(nods))
elif clean:
for nn in nods[:]:
if nn is None:
nods.remove(nn)
if warn is not None:
output(warn + ("%s" % region.name))
return nods
def __call__(self, state0=None, save_results=True, step_hook=None,
post_process_hook=None, nls_status=None):
"""
Solve the time-dependent problem.
"""
problem = self.problem
ts = self.ts
suffix, is_save = prepare_save_data(ts, problem.conf)
if state0 is None:
state0 = get_initial_state(problem)
ii = 0
for step, time in ts:
output(self.format % (time, step + 1, ts.n_step))
state = self.solve_step(ts, state0, nls_status=nls_status)
state0 = state.copy(deep=True)
if step_hook is not None:
step_hook(problem, ts, state)
if save_results and (is_save[ii] == ts.step):
filename = problem.get_output_name(suffix=suffix % ts.step)
problem.save_state(filename, state,
post_process_hook=post_process_hook,
file_per_var=None,
ts=ts)
ii += 1
yield step, time, state
problem.advance(ts)
def __init__(self, conf, **kwargs):
LinearSolver.__init__(self, conf, solve=None, **kwargs)
um = self.sls = None
aux = try_imports(['import scipy.linsolve as sls',
'import scipy.splinalg.dsolve as sls',
'import scipy.sparse.linalg.dsolve as sls'],
'cannot import scipy sparse direct solvers!')
self.sls = aux['sls']
aux = try_imports(['import scipy.linsolve.umfpack as um',
'import scipy.splinalg.dsolve.umfpack as um',
'import scipy.sparse.linalg.dsolve.umfpack as um',
'import scikits.umfpack as um'])
if 'um' in aux:
um = aux['um']
if um is not None:
is_umfpack = hasattr(um, 'UMFPACK_OK')
else:
is_umfpack = False
method = self.conf.method
if method == 'superlu':
self.sls.use_solver(useUmfpack=False)
elif method == 'umfpack':
if not is_umfpack and self.conf.warn:
output('umfpack not available, using superlu!')
elif method != 'auto':
raise ValueError('uknown solution method! (%s)' % method)
if method != 'superlu' and is_umfpack:
self.sls.use_solver(useUmfpack=True,
assumeSortedIndices=True)
def main():
from sfepy.base.base import output
from sfepy.base.conf import ProblemConf, get_standard_keywords
from sfepy.fem import ProblemDefinition
from sfepy.applications import solve_evolutionary
output.prefix = 'therel:'
required, other = get_standard_keywords()
conf = ProblemConf.from_file(__file__, required, other)
problem = ProblemDefinition.from_conf(conf, init_equations=False)
# Setup output directory according to options above.
problem.setup_default_output()
# First solve the stationary electric conduction problem.
problem.set_equations({'eq' : conf.equations['1']})
problem.time_update()
state_el = problem.solve()
problem.save_state(problem.get_output_name(suffix = 'el'), state_el)
# Then solve the evolutionary heat conduction problem, using state_el.
problem.set_equations({'eq' : conf.equations['2']})
phi_var = problem.get_variables()['phi_known']
phi_var.data_from_any(state_el())
solve_evolutionary(problem)
output('results saved in %s' % problem.get_output_name(suffix = '*'))
def __call__(self,
rhs,
x0=None,
conf=None,
eps_a=None,
eps_r=None,
i_max=None,
mtx=None,
status=None,
**kwargs):
import os, sys, shutil, tempfile
from sfepy import base_dir
from sfepy.base.ioutils import ensure_path
eps_a = get_default(eps_a, self.conf.eps_a)
eps_r = get_default(eps_r, self.conf.eps_r)
i_max = get_default(i_max, self.conf.i_max)
eps_d = self.conf.eps_d
petsc = self.petsc
# There is no use in caching matrix in the solver - always set as new.
pmtx, psol, prhs = self.set_matrix(mtx)
ksp = self.ksp
ksp.setOperators(pmtx)
ksp.setFromOptions() # PETSc.Options() not used yet...
ksp.setTolerances(atol=eps_a, rtol=eps_r, divtol=eps_d, max_it=i_max)
output_dir = tempfile.mkdtemp()
# Set PETSc rhs, solve, get solution from PETSc solution.
if x0 is not None:
psol[...] = x0
sol0_filename = os.path.join(output_dir, 'sol0.dat')
else:
sol0_filename = ''
prhs[...] = rhs
script_filename = os.path.join(base_dir, 'solvers/petsc_worker.py')
mtx_filename = os.path.join(output_dir, 'mtx.dat')
rhs_filename = os.path.join(output_dir, 'rhs.dat')
sol_filename = os.path.join(output_dir, 'sol.dat')
status_filename = os.path.join(output_dir, 'status.txt')
log_filename = os.path.join(self.conf.log_dir, 'sol.log')
ensure_path(log_filename)
output('storing system to %s...' % output_dir)
tt = time.clock()
view_mtx = petsc.Viewer().createBinary(mtx_filename, mode='w')
view_rhs = petsc.Viewer().createBinary(rhs_filename, mode='w')
pmtx.view(view_mtx)
prhs.view(view_rhs)
if sol0_filename:
view_sol0 = petsc.Viewer().createBinary(sol0_filename, mode='w')
psol.view(view_sol0)
output('...done in %.2f s' % (time.clock() - tt))
command = [
'mpiexec -n %d' % self.conf.n_proc,
sys.executable,
script_filename,
'-mtx %s' % mtx_filename,
'-rhs %s' % rhs_filename,
'-sol0 %s' % sol0_filename,
'-sol %s' % sol_filename,
'-status %s' % status_filename,
'-ksp_type %s' % self.conf.method,
'-pc_type %s' % self.conf.precond,
'-sub_pc_type %s' % self.conf.sub_precond,
'-ksp_atol %.3e' % self.conf.eps_a,
'-ksp_rtol %.3e' % self.conf.eps_r,
'-ksp_max_it %d' % self.conf.i_max,
'-ksp_monitor %s' % log_filename,
'-ksp_view %s' % log_filename,
]
if self.conf.precond_side is not None:
command.append('-ksp_pc_side %s' % self.conf.precond_side)
out = os.system(" ".join(command))
assert_(out == 0)
output('reading solution...')
tt = time.clock()
view_sol = self.petsc.Viewer().createBinary(sol_filename, mode='r')
psol = petsc.Vec().load(view_sol)
fd = open(status_filename, 'r')
line = fd.readline().split()
reason = int(line[0])
elapsed = float(line[1])
fd.close()
output('...done in %.2f s' % (time.clock() - tt))
sol = psol[...].copy()
output('%s(%s, %s/proc) convergence: %s (%s)' %
(self.conf.method, self.conf.precond, self.conf.sub_precond,
reason, self.converged_reasons[reason]))
output('elapsed: %.2f [s]' % elapsed)
shutil.rmtree(output_dir)
return sol
def gen_cylinder_mesh(dims,
shape,
centre,
axis='x',
force_hollow=False,
is_open=False,
open_angle=0.0,
non_uniform=False,
name='cylinder',
verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle + (nfi) * dfi, nfi + 1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr, ), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii - 1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii - 1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix, iy, iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix, iy, iz] = grid[ix, 0, iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nnfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr - 1, nnfi, nl - 1]):
if iy < (nnfi - 1):
conn[ii, :] = [
grid[ix, iy, iz], grid[ix + 1, iy, iz], grid[ix + 1, iy + 1,
iz],
grid[ix, iy + 1, iz], grid[ix, iy, iz + 1], grid[ix + 1, iy,
iz + 1],
grid[ix + 1, iy + 1, iz + 1], grid[ix, iy + 1, iz + 1]
]
ii += 1
elif not is_open:
conn[ii, :] = [
grid[ix, iy, iz], grid[ix + 1, iy, iz], grid[ix + 1, 0, iz],
grid[ix, 0, iz], grid[ix, iy, iz + 1],
grid[ix + 1, iy, iz + 1], grid[ix + 1, 0, iz + 1], grid[ix, 0,
iz + 1]
]
ii += 1
mat_id = nm.zeros((n_el, ), dtype=nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:, [1, 2, 0]]
elif axis == 'y':
coors = coors[:, [2, 0, 1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def __call__(self,
rhs,
x0=None,
conf=None,
eps_a=None,
eps_r=None,
i_max=None,
mtx=None,
status=None,
comm=None,
context=None,
**kwargs):
eps_a = get_default(eps_a, self.conf.eps_a)
eps_r = get_default(eps_r, self.conf.eps_r)
i_max = get_default(i_max, self.conf.i_max)
eps_d = self.conf.eps_d
if self.mtx_id == id(mtx):
ksp = self.ksp
pmtx = self.pmtx
else:
pmtx = self.create_petsc_matrix(mtx, comm=comm)
ksp = self.create_ksp(comm=comm)
ksp.setOperators(pmtx)
ksp.setTolerances(atol=eps_a,
rtol=eps_r,
divtol=eps_d,
max_it=i_max)
setup_precond = self.conf.setup_precond
if setup_precond is not None:
ksp.pc.setPythonContext(setup_precond(mtx, context))
ksp.setFromOptions()
self.mtx_id = id(mtx)
self.ksp = ksp
self.pmtx = pmtx
if isinstance(rhs, self.petsc.Vec):
prhs = rhs
else:
prhs = pmtx.getVecLeft()
prhs[...] = rhs
if x0 is not None:
if isinstance(x0, self.petsc.Vec):
psol = x0
else:
psol = pmtx.getVecRight()
psol[...] = x0
ksp.setInitialGuessNonzero(True)
else:
psol = pmtx.getVecRight()
ksp.setInitialGuessNonzero(False)
ksp.solve(prhs, psol)
output('%s(%s, %s/proc) convergence: %s (%s, %d iterations)' %
(ksp.getType(), ksp.getPC().getType(), self.conf.sub_precond,
ksp.reason, self.converged_reasons[ksp.reason],
ksp.getIterationNumber()),
verbose=conf.verbose)
if isinstance(rhs, self.petsc.Vec):
sol = psol
else:
sol = psol[...].copy()
return sol
def distribute_field_dofs(field,
gfd,
use_expand_dofs=False,
comm=None,
verbose=False):
"""
Distribute the owned cells and DOFs of the given field to all tasks.
The DOFs use the PETSc ordering and are in form of a connectivity, so that
each task can easily identify them with the DOFs of the original global
ordering or local ordering.
"""
if comm is None:
comm = PETSc.COMM_WORLD
size = comm.size
mpi = comm.tompi4py()
if comm.rank == 0:
dof_maps = gfd.dof_maps
id_map = gfd.id_map
# Send subdomain data to other tasks.
for it in range(1, size):
# Send owned and overlap cells.
cells = nm.union1d(gfd.cell_parts[it], gfd.overlap_cells[it])
mpi.send(len(cells), it)
mpi.Send([cells, MPI.INTEGER4], it)
dof_map = dof_maps[it]
# Send owned petsc_dofs range.
mpi.send(gfd.coffsets[it], it)
mpi.send(gfd.coffsets[it] + dof_map[3], it)
# Send petsc_dofs of global_dofs.
global_dofs = field.econn[cells]
if use_expand_dofs:
global_dofs = expand_dofs(global_dofs, field.n_components)
petsc_dofs_conn = id_map[global_dofs]
mpi.send(petsc_dofs_conn.shape[0], it)
mpi.send(petsc_dofs_conn.shape[1], it)
mpi.Send([petsc_dofs_conn, MPI.INTEGER4], it)
cells = nm.union1d(gfd.cell_parts[0], gfd.overlap_cells[0])
n_cell = len(cells)
global_dofs = field.econn[cells]
if use_expand_dofs:
global_dofs = expand_dofs(global_dofs, field.n_components)
dof_map = dof_maps[0]
petsc_dofs_range = (gfd.coffsets[0], gfd.coffsets[0] + dof_map[3])
petsc_dofs_conn = id_map[global_dofs]
else:
# Receive owned cells.
n_cell = mpi.recv(source=0)
cells = nm.empty(n_cell, dtype=nm.int32)
mpi.Recv([cells, MPI.INTEGER4], source=0)
# Receive owned petsc_dofs range.
i0 = mpi.recv(source=0)
i1 = mpi.recv(source=0)
petsc_dofs_range = (i0, i1)
# Receive petsc_dofs of global_dofs.
n_cell = mpi.recv(source=0)
n_cdof = mpi.recv(source=0)
petsc_dofs_conn = nm.empty((n_cell, n_cdof), dtype=nm.int32)
mpi.Recv([petsc_dofs_conn, MPI.INTEGER4], source=0)
dof_maps = id_map = None
if verbose:
output('n_cell:', n_cell)
output('cells:', cells)
output('owned petsc DOF range:', petsc_dofs_range,
petsc_dofs_range[1] - petsc_dofs_range[0])
aux = nm.unique(petsc_dofs_conn)
output('local petsc DOFs (owned + shared):', aux, len(aux))
return cells, petsc_dofs_range, petsc_dofs_conn, dof_maps, id_map
def recover_micro_hook_eps(micro_filename,
region,
eval_var,
nodal_values,
const_values,
eps0,
recovery_file_tag='',
define_args=None,
verbose=False,
use_cache=False):
# Create a micro-problem instance.
required, other = get_standard_keywords()
required.remove('equations')
conf = ProblemConf.from_file(micro_filename,
required,
other,
verbose=False,
define_args=define_args)
coefs_filename = conf.options.get('coefs_filename', 'coefs')
output_dir = conf.options.get('output_dir', '.')
coefs_filename = op.join(output_dir, coefs_filename) + '.h5'
if not use_cache:
cc_cache.clear()
# Coefficients and correctors
if coefs_filename not in cc_cache:
coefs = Coefficients.from_file_hdf5(coefs_filename)
corrs = get_correctors_from_file_hdf5(dump_names=coefs.save_names)
cc_cache[coefs_filename] = coefs, corrs
else:
coefs, corrs = cc_cache[coefs_filename]
recovery_hook = conf.options.get('recovery_hook', None)
if recovery_hook is not None:
recovery_hook = conf.get_function(recovery_hook)
pb = Problem.from_conf(conf, init_equations=False, init_solvers=False)
# Get tiling of a given region
rcoors = region.domain.mesh.coors[region.get_entities(0), :]
rcmin = nm.min(rcoors, axis=0)
rcmax = nm.max(rcoors, axis=0)
nn = nm.round((rcmax - rcmin) / eps0)
if nm.prod(nn) == 0:
output('inconsistency in recovery region and microstructure size!')
return
cs = []
for ii, n in enumerate(nn):
cs.append(nm.arange(n) * eps0 + rcmin[ii])
x0 = nm.empty((int(nm.prod(nn)), nn.shape[0]), dtype=nm.float64)
for ii, icoor in enumerate(nm.meshgrid(*cs, indexing='ij')):
x0[:, ii] = icoor.flatten()
mesh = pb.domain.mesh
coors, conn, outs, ndoffset = [], [], [], 0
# Recover region
mic_coors = (mesh.coors - mesh.get_bounding_box()[0, :]) * eps0
evfield = eval_var.field
output('recovering microsctructures...')
timer = Timer(start=True)
output_fun = output.output_function
output_level = output.level
for ii, c0 in enumerate(x0):
local_macro = {'eps0': eps0}
local_coors = mic_coors + c0
# Inside recovery region?
v = nm.ones((evfield.region.entities[0].shape[0], 1))
v[evfield.vertex_remap[region.entities[0]]] = 0
no = nm.sum(v)
aux = evfield.evaluate_at(local_coors, v)
if no > 0 and (nm.sum(aux) / no) > 1e-3:
continue
output.level = output_level
output('micro: %d / %d' % (ii, x0.shape[0]))
for k, v in six.iteritems(nodal_values):
local_macro[k] = evfield.evaluate_at(local_coors, v)
for k, v in six.iteritems(const_values):
local_macro[k] = v
output.set_output(quiet=not (verbose))
outs.append(recovery_hook(pb, corrs, local_macro))
output.output_function = output_fun
coors.append(local_coors)
conn.append(mesh.get_conn(mesh.descs[0]) + ndoffset)
ndoffset += mesh.n_nod
output('...done in %.2f s' % timer.stop())
# Collect output variables
outvars = {}
for k, v in six.iteritems(outs[0]):
if v.var_name in outvars:
outvars[v.var_name].append(k)
else:
outvars[v.var_name] = [k]
# Split output by variables/regions
pvs = pb.create_variables(outvars.keys())
outregs = {k: pvs[k].field.region.get_entities(-1) for k in outvars.keys()}
nrve = len(coors)
coors = nm.vstack(coors)
ngroups = nm.tile(mesh.cmesh.vertex_groups.squeeze(), (nrve, ))
conn = nm.vstack(conn)
cgroups = nm.tile(mesh.cmesh.cell_groups.squeeze(), (nrve, ))
# Get region mesh and data
for k, cidxs in six.iteritems(outregs):
gcidxs = nm.hstack([cidxs + mesh.n_el * ii for ii in range(nrve)])
rconn = conn[gcidxs]
remap = -nm.ones((coors.shape[0], ), dtype=nm.int32)
remap[rconn] = 1
vidxs = nm.where(remap > 0)[0]
remap[vidxs] = nm.arange(len(vidxs))
rconn = remap[rconn]
rcoors = coors[vidxs, :]
out = {}
for ifield in outvars[k]:
data = [outs[ii][ifield].data for ii in range(nrve)]
out[ifield] = Struct(name='output_data',
mode=outs[0][ifield].mode,
dofs=None,
var_name=k,
data=nm.vstack(data))
micro_name = pb.get_output_name(extra='recovered%s_%s' %
(recovery_file_tag, k))
filename = op.join(output_dir, op.basename(micro_name))
mesh_out = Mesh.from_data('recovery_%s' % k, rcoors, ngroups[vidxs],
[rconn], [cgroups[gcidxs]], [mesh.descs[0]])
mesh_out.write(filename, io='auto', out=out)
def recover_micro_hook(micro_filename,
region,
macro,
naming_scheme='step_iel',
recovery_file_tag='',
define_args=None,
verbose=False):
# Create a micro-problem instance.
required, other = get_standard_keywords()
required.remove('equations')
conf = ProblemConf.from_file(micro_filename,
required,
other,
verbose=False,
define_args=define_args)
coefs_filename = conf.options.get('coefs_filename', 'coefs')
output_dir = conf.options.get('output_dir', '.')
coefs_filename = op.join(output_dir, coefs_filename) + '.h5'
# Coefficients and correctors
coefs = Coefficients.from_file_hdf5(coefs_filename)
corrs = get_correctors_from_file_hdf5(dump_names=coefs.save_names)
recovery_hook = conf.options.get('recovery_hook', None)
if recovery_hook is not None:
recovery_hook = conf.get_function(recovery_hook)
pb = Problem.from_conf(conf, init_equations=False, init_solvers=False)
format = get_print_info(pb.domain.mesh.n_el, fill='0')[1]
output('recovering microsctructures...')
timer = Timer(start=True)
output_fun = output.output_function
output_level = output.level
for ii, iel in enumerate(region.cells):
output.level = output_level
output('micro: %d (el=%d)' % (ii, iel))
local_macro = {}
for k, v in six.iteritems(macro):
local_macro[k] = v[ii, 0]
output.set_output(quiet=not (verbose))
out = recovery_hook(pb, corrs, local_macro)
output.output_function = output_fun
if ii == 0:
new_keys = []
new_data = {}
new_idxs = []
for k in six.iterkeys(local_macro):
if k not in macro:
new_keys.append(k)
new_data[k] = []
new_idxs.append(ii)
for jj in new_keys:
new_data[jj].append(local_macro[jj])
# save data
if out is not None:
suffix = format % iel
micro_name = pb.get_output_name(extra='recovered_' +
recovery_file_tag + suffix)
filename = op.join(output_dir, op.basename(micro_name))
fpv = pb.conf.options.get('file_per_var', False)
pb.save_state(filename, out=out, file_per_var=fpv)
output('...done in %.2f s' % timer.stop())
for jj in new_keys:
lout = new_data[jj]
macro[jj] = nm.zeros((nm.max(new_idxs) + 1, 1) + lout[0].shape,
dtype=lout[0].dtype)
out = macro[jj]
for kk, ii in enumerate(new_idxs):
out[ii, 0] = lout[kk]
def assemble_mtx_to_petsc(pmtx,
mtx,
pdofs,
drange,
is_overlap=True,
comm=None,
verbose=False):
"""
Assemble a local CSR matrix to a global PETSc matrix.
WIP
---
Try Mat.setValuesCSR() - no lgmap - filtering vectorized?
"""
if comm is None:
comm = PETSc.COMM_WORLD
lgmap = PETSc.LGMap().create(pdofs, comm=comm)
if is_overlap:
pmtx.setLGMap(lgmap, lgmap)
data, prows, cols = mtx.data, mtx.indptr, mtx.indices
output('setting matrix values...', verbose=verbose)
tt = time.clock()
for ir, rdof in enumerate(pdofs):
if (rdof < drange[0]) or (rdof >= drange[1]): continue
for ic in range(prows[ir], prows[ir + 1]):
# output(ir, rdof, cols[ic])
pmtx.setValueLocal(ir, cols[ic], data[ic],
PETSc.InsertMode.INSERT_VALUES)
output('...done in', time.clock() - tt, verbose=verbose)
output('assembling matrix...', verbose=verbose)
tt = time.clock()
pmtx.assemble()
output('...done in', time.clock() - tt, verbose=verbose)
else:
pmtx.setLGMap(lgmap, lgmap)
output('setting matrix values...', verbose=verbose)
tt = time.clock()
pmtx.setValuesLocalCSR(mtx.indptr, mtx.indices, mtx.data,
PETSc.InsertMode.ADD_VALUES)
output('...done in', time.clock() - tt, verbose=verbose)
output('assembling matrix...', verbose=verbose)
tt = time.clock()
pmtx.assemble()
output('...done in', time.clock() - tt, verbose=verbose)
def assemble_rhs_to_petsc(prhs,
rhs,
pdofs,
drange,
is_overlap=True,
comm=None,
verbose=False):
"""
Assemble a local right-hand side vector to a global PETSc vector.
"""
if comm is None:
comm = PETSc.COMM_WORLD
lgmap = PETSc.LGMap().create(pdofs, comm=comm)
if is_overlap:
prhs.setLGMap(lgmap)
output('setting rhs values...', verbose=verbose)
tt = time.clock()
for ir, rdof in enumerate(pdofs):
if (rdof < drange[0]) or (rdof >= drange[1]): continue
prhs.setValueLocal(ir, rhs[ir], PETSc.InsertMode.INSERT_VALUES)
output('...done in', time.clock() - tt, verbose=verbose)
output('assembling rhs...', verbose=verbose)
tt = time.clock()
prhs.assemble()
output('...done in', time.clock() - tt, verbose=verbose)
else:
prhs.setLGMap(lgmap)
output('setting rhs values...', verbose=verbose)
tt = time.clock()
prhs.setValuesLocal(nm.arange(len(rhs), dtype=nm.int32), rhs,
PETSc.InsertMode.ADD_VALUES)
output('...done in', time.clock() - tt, verbose=verbose)
output('assembling rhs...', verbose=verbose)
tt = time.clock()
prhs.assemble()
output('...done in', time.clock() - tt, verbose=verbose)
def setup_composite_dofs(lfds, fields, local_variables, verbose=False):
"""
Setup composite DOFs built from field blocks described by `lfds` local
field distributions information.
Returns (local, total) sizes of a vector, local equation range for a
composite matrix, and the local ordering of composite PETSc DOFs,
corresponding to `local_variables` (must be in the order of `fields`!).
"""
for ii, variable in enumerate(local_variables.iter_state(ordered=True)):
output('field %s:' % fields[ii].name, verbose=verbose)
lfd = lfds[ii]
output('PETSc DOFs range:', lfd.petsc_dofs_range, verbose=verbose)
n_cdof = fields[ii].n_nod * fields[ii].n_components
lfd.sizes, lfd.drange = get_sizes(lfd.petsc_dofs_range, n_cdof, 1)
output('sizes, drange:', lfd.sizes, lfd.drange, verbose=verbose)
lfd.petsc_dofs = get_local_ordering(variable.field,
lfd.petsc_dofs_conn,
use_expand_dofs=True)
output('petsc dofs:', lfd.petsc_dofs, verbose=verbose)
sizes, drange = get_composite_sizes(lfds)
output('composite sizes:', sizes, verbose=verbose)
output('composite drange:', drange, verbose=verbose)
pdofs = nm.concatenate([ii.petsc_dofs for ii in lfds])
output('composite pdofs:', pdofs, verbose=verbose)
return sizes, drange, pdofs
def distribute_fields_dofs(fields,
cell_tasks,
is_overlap=True,
use_expand_dofs=False,
comm=None,
verbose=False):
"""
Distribute the owned cells and DOFs of the given field to all tasks.
Uses interleaved PETSc numbering in each task, i.e., the PETSc DOFs of each
tasks are consecutive and correspond to the first field DOFs block followed
by the second etc.
Expand DOFs to equations if `use_expand_dofs` is True.
"""
if comm is None:
comm = PETSc.COMM_WORLD
size = comm.size
if comm.rank == 0:
gfds = []
inter_facets = get_inter_facets(fields[0].domain, cell_tasks)
for field in fields:
aux = create_task_dof_maps(field,
cell_tasks,
inter_facets,
is_overlap=is_overlap,
use_expand_dofs=use_expand_dofs)
cell_parts = aux[2]
n_cell_parts = [len(ii) for ii in cell_parts]
output('numbers of cells in tasks (without overlaps):',
n_cell_parts,
verbose=verbose)
assert_(sum(n_cell_parts) == field.domain.mesh.n_el)
assert_(nm.all(n_cell_parts > 0))
gfd = Struct(name='global field %s distribution' % field.name,
dof_maps=aux[0],
id_map=aux[1],
cell_parts=aux[2],
overlap_cells=aux[3],
coffsets=nm.empty(size, dtype=nm.int32))
gfds.append(gfd)
# Initialize composite offsets of DOFs.
if len(fields) > 1:
# Renumber id_maps for field inter-leaving.
offset = 0
for ir in range(size):
for ii, gfd in enumerate(gfds):
dof_map = gfd.dof_maps[ir]
n_owned = dof_map[3]
off = dof_map[4]
iown = nm.concatenate([dof_map[0]] + dof_map[1])
gfd.id_map[iown] += offset - off
gfd.coffsets[ir] = offset
offset += n_owned
else:
gfd = gfds[0]
gfd.coffsets[:] = [gfd.dof_maps[ir][4] for ir in range(size)]
else:
gfds = [None] * len(fields)
lfds = []
for ii, field in enumerate(fields):
aux = distribute_field_dofs(field,
gfds[ii],
use_expand_dofs=use_expand_dofs,
comm=comm,
verbose=verbose)
lfd = Struct(name='local field %s distribution' % field.name,
cells=aux[0],
petsc_dofs_range=aux[1],
petsc_dofs_conn=aux[2])
lfds.append(lfd)
return lfds, gfds
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s',
'--scale',
metavar='scale',
action='store',
dest='scale',
default=None,
help=help['scale'])
parser.add_argument('-c',
'--center',
metavar='center',
action='store',
dest='center',
default=None,
help=help['center'])
parser.add_argument('-r',
'--refine',
metavar='level',
action='store',
type=int,
dest='refine',
default=0,
help=help['refine'])
parser.add_argument('-f',
'--format',
metavar='format',
action='store',
type=str,
dest='format',
default=None,
help=help['format'])
parser.add_argument('-l',
'--list',
action='store_true',
dest='list',
help=help['list'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
mesh = Mesh.from_file(filename_in)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements' %
(domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements' %
(domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
io = MeshIO.for_format(filename_out, format=options.format, writable=True)
cell_types = ', '.join(supported_cell_types[io.format])
output('writing [%s] %s...' % (cell_types, filename_out))
mesh.write(filename_out, io=io)
output('...done')
def verify_task_dof_maps(dof_maps,
id_map,
field,
use_expand_dofs=False,
verbose=False):
"""
Verify the counts and values of DOFs in `dof_maps` and `id_map`
corresponding to `field`.
Returns the vector with a task number for each DOF.
"""
tt = time.clock()
if verbose:
output('verifying...')
output('total number of DOFs:', field.n_nod)
output('number of tasks:', len(dof_maps))
count = count2 = 0
dofs = []
if use_expand_dofs:
vec = nm.empty(field.n_nod * field.n_components, dtype=nm.float64)
else:
vec = nm.empty(field.n_nod, dtype=nm.float64)
for ir, dof_map in ordered_iteritems(dof_maps):
n_owned = dof_map[3]
offset = dof_map[4]
o2 = offset + n_owned
if verbose:
output('task %d: %d owned on offset %d' % (ir, n_owned, offset))
if not use_expand_dofs:
aux = dof_map[0]
assert_(nm.all((id_map[aux] >= offset) & (id_map[aux] < o2)))
count2 += dof_map[3]
count += len(dof_map[0])
dofs.append(dof_map[0])
vec[dof_map[0]] = ir
for aux in dof_map[1]:
if not use_expand_dofs:
assert_(nm.all((id_map[aux] >= offset) & (id_map[aux] < o2)))
count += len(aux)
dofs.append(aux)
vec[aux] = ir
dofs = nm.concatenate(dofs)
n_dof = vec.shape[0]
assert_(n_dof == len(dofs))
if not expand_dofs:
assert_(nm.all(nm.sort(dofs) == nm.sort(id_map)))
dofs = nm.unique(dofs)
assert_(n_dof == len(dofs))
assert_(n_dof == dofs[-1] + 1)
assert_(n_dof == count)
assert_(n_dof == count2)
assert_(n_dof == len(id_map))
assert_(n_dof == len(nm.unique(id_map)))
output('...done in', time.clock() - tt, verbose=verbose)
return vec
def evaluate_at(self, coors, source_vals, mode='val', strategy='general',
close_limit=0.1, get_cells_fun=None, cache=None,
ret_cells=False, ret_status=False, ret_ref_coors=False,
verbose=False):
"""
Evaluate source DOF values corresponding to the field in the given
coordinates using the field interpolation.
Parameters
----------
coors : array, shape ``(n_coor, dim)``
The coordinates the source values should be interpolated into.
source_vals : array, shape ``(n_nod, n_components)``
The source DOF values corresponding to the field.
mode : {'val', 'grad'}, optional
The evaluation mode: the field value (default) or the field value
gradient.
strategy : {'general', 'convex'}, optional
The strategy for finding the elements that contain the
coordinates. For convex meshes, the 'convex' strategy might be
faster than the 'general' one.
close_limit : float, optional
The maximum limit distance of a point from the closest
element allowed for extrapolation.
get_cells_fun : callable, optional
If given, a function with signature ``get_cells_fun(coors, cmesh,
**kwargs)`` returning cells and offsets that potentially contain
points with the coordinates `coors`. Applicable only when
`strategy` is 'general'. When not given,
:func:`get_potential_cells()
<sfepy.discrete.common.global_interp.get_potential_cells>` is used.
cache : Struct, optional
To speed up a sequence of evaluations, the field mesh and other
data can be cached. Optionally, the cache can also contain the
reference element coordinates as `cache.ref_coors`, `cache.cells`
and `cache.status`, if the evaluation occurs in the same
coordinates repeatedly. In that case the mesh related data are
ignored. See :func:`Field.get_evaluate_cache()
<sfepy.discrete.fem.fields_base.FEField.get_evaluate_cache()>`.
ret_ref_coors : bool, optional
If True, return also the found reference element coordinates.
ret_status : bool, optional
If True, return also the enclosing cell status for each point.
ret_cells : bool, optional
If True, return also the cell indices the coordinates are in.
verbose : bool
If False, reduce verbosity.
Returns
-------
vals : array
The interpolated values with shape ``(n_coor, n_components)`` or
gradients with shape ``(n_coor, n_components, dim)`` according to
the `mode`. If `ret_status` is False, the values where the status
is greater than one are set to ``numpy.nan``.
ref_coors : array
The found reference element coordinates, if `ret_ref_coors` is True.
cells : array
The cell indices, if `ret_ref_coors` or `ret_cells` or `ret_status`
are True.
status : array
The status, if `ret_ref_coors` or `ret_status` are True, with the
following meaning: 0 is success, 1 is extrapolation within
`close_limit`, 2 is extrapolation outside `close_limit`, 3 is
failure, 4 is failure due to non-convergence of the Newton
iteration in tensor product cells. If close_limit is 0, then for
the 'general' strategy the status 5 indicates points outside of the
field domain that had no potential cells.
"""
from sfepy.discrete.common.global_interp import get_ref_coors
from sfepy.discrete.common.extmods.crefcoors import evaluate_in_rc
from sfepy.base.base import complex_types
output('evaluating in %d points...' % coors.shape[0], verbose=verbose)
ref_coors, cells, status = get_ref_coors(self, coors,
strategy=strategy,
close_limit=close_limit,
get_cells_fun=get_cells_fun,
cache=cache,
verbose=verbose)
timer = Timer(start=True)
# Interpolate to the reference coordinates.
source_dtype = nm.float64 if source_vals.dtype in complex_types\
else source_vals.dtype
if mode == 'val':
vals = nm.empty((coors.shape[0], source_vals.shape[1], 1),
dtype=source_dtype)
cmode = 0
elif mode == 'grad':
vals = nm.empty((coors.shape[0], source_vals.shape[1],
coors.shape[1]),
dtype=source_dtype)
cmode = 1
ctx = self.create_basis_context()
if source_vals.dtype in complex_types:
valsi = vals.copy()
evaluate_in_rc(vals, ref_coors, cells, status,
nm.ascontiguousarray(source_vals.real),
self.get_econn('volume', self.region), cmode, ctx)
evaluate_in_rc(valsi, ref_coors, cells, status,
nm.ascontiguousarray(source_vals.imag),
self.get_econn('volume', self.region), cmode, ctx)
vals = vals + valsi * 1j
else:
evaluate_in_rc(vals, ref_coors, cells, status, source_vals,
self.get_econn('volume', self.region), cmode, ctx)
output('interpolation: %f s' % timer.stop(),verbose=verbose)
output('...done',verbose=verbose)
if mode == 'val':
vals.shape = (coors.shape[0], source_vals.shape[1])
if not ret_status:
ii = nm.where(status > 1)[0]
vals[ii] = nm.nan
if ret_ref_coors:
return vals, ref_coors, cells, status
elif ret_status:
return vals, cells, status
elif ret_cells:
return vals, cells
else:
return vals
def solve_eigen_problem(self):
opts = self.app_options
pb = self.problem
pb.set_equations(pb.conf.equations)
pb.time_update()
output('assembling lhs...')
timer = Timer(start=True)
mtx_a = pb.evaluate(pb.conf.equations['lhs'], mode='weak',
auto_init=True, dw_mode='matrix')
output('...done in %.2f s' % timer.stop())
if 'rhs' in pb.conf.equations:
output('assembling rhs...')
timer.start()
mtx_b = pb.evaluate(pb.conf.equations['rhs'], mode='weak',
dw_mode='matrix')
output('...done in %.2f s' % timer.stop())
else:
mtx_b = None
_n_eigs = get_default(opts.n_eigs, mtx_a.shape[0])
output('solving eigenvalue problem for {} values...'.format(_n_eigs))
eig = Solver.any_from_conf(pb.get_solver_conf(opts.evps))
if opts.eigs_only:
eigs = eig(mtx_a, mtx_b, opts.n_eigs, eigenvectors=False)
svecs = None
else:
eigs, svecs = eig(mtx_a, mtx_b, opts.n_eigs, eigenvectors=True)
output('...done')
vecs = self.make_full(svecs)
self.save_results(eigs, vecs)
return Struct(pb=pb, eigs=eigs, vecs=vecs)
def make_global_operator(self, adi, new_only=False):
"""
Assemble all LCBC operators into a single matrix.
Parameters
----------
adi : DofInfo
The active DOF information.
new_only : bool
If True, the operator columns will contain only new DOFs.
Returns
-------
mtx_lc : csr_matrix
The global LCBC operator in the form of a CSR matrix.
rhs_lc : array
The right-hand side for non-homogeneous LCBCs.
lcdi : DofInfo
The global active LCBC-constrained DOF information.
"""
self.finalize()
if len(self) == 0: return (None,) * 3
n_dof = self.variables.adi.ptr[-1]
n_constrained = nm.sum([val for val in self.n_master.itervalues()])
n_dof_free = nm.sum([val for val in self.n_free.itervalues()])
n_dof_new = nm.sum([val for val in self.n_new.itervalues()])
n_dof_active = nm.sum([val for val in self.n_active.itervalues()])
output('dofs: total %d, free %d, constrained %d, new %d'\
% (n_dof, n_dof_free, n_constrained, n_dof_new))
output(' -> active %d' % (n_dof_active))
adi = self.variables.adi
lcdi, ndi, fdi = self.lcdi, self.ndi, self.fdi
rows = []
cols = []
data = []
lcbc_mask = nm.ones(n_dof, dtype=nm.bool)
is_homogeneous = True
for ii, op in enumerate(self):
rvar_name = op.var_names[0]
roff = adi.indx[rvar_name].start
irs = roff + op.ameq
lcbc_mask[irs] = False
if op.get('rhs', None) is not None:
is_homogeneous = False
if not is_homogeneous:
vec_lc = nm.zeros(n_dof, dtype=nm.float64)
else:
vec_lc = None
for ii, op in enumerate(self):
rvar_name = op.var_names[0]
roff = adi.indx[rvar_name].start
irs = roff + op.ameq
cvar_name = op.var_names[1]
if cvar_name is None:
if new_only:
coff = ndi.indx[rvar_name].start
else:
coff = lcdi.indx[rvar_name].start + fdi.n_dof[rvar_name]
iis, icols = self.ics[rvar_name]
ici = nm.searchsorted(iis, ii)
ics = nm.arange(coff + icols[ici], coff + icols[ici+1])
if isinstance(op.mtx, sp.spmatrix):
lr, lc, lv = sp.find(op.mtx)
rows.append(irs[lr])
cols.append(ics[lc])
data.append(lv)
else:
_irs, _ics = nm.meshgrid(irs, ics)
rows.append(_irs.ravel())
cols.append(_ics.ravel())
data.append(op.mtx.T.ravel())
else:
coff = lcdi.indx[cvar_name].start
lr, lc, lv = sp.find(op.mtx)
ii1 = nm.where(lcbc_mask[adi.indx[cvar_name]])[0]
ii2 = nm.searchsorted(ii1, lc)
rows.append(roff + lr)
cols.append(coff + ii2)
data.append(lv)
if vec_lc is not None:
vec_lc[irs] += op.get('rhs', 0)
rows = nm.concatenate(rows)
cols = nm.concatenate(cols)
data = nm.concatenate(data)
if new_only:
mtx_lc = sp.coo_matrix((data, (rows, cols)),
shape=(n_dof, n_dof_new))
else:
mtx_lc = sp.coo_matrix((data, (rows, cols)),
shape=(n_dof, n_dof_active))
ir = nm.where(lcbc_mask)[0]
ic = nm.empty((n_dof_free,), dtype=nm.int32)
for var_name in adi.var_names:
ii = nm.arange(fdi.n_dof[var_name], dtype=nm.int32)
ic[fdi.indx[var_name]] = lcdi.indx[var_name].start + ii
mtx_lc2 = sp.coo_matrix((nm.ones((ir.shape[0],)), (ir, ic)),
shape=(n_dof, n_dof_active),
dtype=nm.float64)
mtx_lc = mtx_lc + mtx_lc2
mtx_lc = mtx_lc.tocsr()
return mtx_lc, vec_lc, lcdi
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('-d', '--dims', metavar='l,w,t',
action='store', dest='dims',
default='0.2,0.01,0.001', help=helps['dims'])
parser.add_argument('-n', '--nx', metavar='start,stop,step',
action='store', dest='nx',
default='2,103,10', help=helps['nx'])
parser.add_argument('-t', '--transform', choices=['none', 'bend', 'twist'],
action='store', dest='transform',
default='none', help=helps['transform'])
parser.add_argument('--young', metavar='float', type=float,
action='store', dest='young',
default=210e9, help=helps['young'])
parser.add_argument('--poisson', metavar='float', type=float,
action='store', dest='poisson',
default=0.3, help=helps['poisson'])
parser.add_argument('--force', metavar='float', type=float,
action='store', dest='force',
default=-1.0, help=helps['force'])
parser.add_argument('-p', '--plot',
action="store_true", dest='plot',
default=False, help=helps['plot'])
parser.add_argument('--u-scaling', metavar='float', type=float,
action='store', dest='scaling',
default=1.0, help=helps['scaling'])
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
options = parser.parse_args()
dims = nm.array([float(ii) for ii in options.dims.split(',')],
dtype=nm.float64)
nxs = tuple([int(ii) for ii in options.nx.split(',')])
young = options.young
poisson = options.poisson
force = options.force
output_dir = options.output_dir
odir = lambda filename: os.path.join(output_dir, filename)
filename = odir('output_log.txt')
ensure_path(filename)
output.set_output(filename=filename, combined=options.silent == False)
output('output directory:', output_dir)
output('using values:')
output(" dimensions:", dims)
output(" nx range:", nxs)
output(" Young's modulus:", options.young)
output(" Poisson's ratio:", options.poisson)
output(' force:', options.force)
output(' transform:', options.transform)
if options.transform == 'none':
options.transform = None
u_exact = get_analytical_displacement(dims, young, force,
transform=options.transform)
if options.transform is None:
ilog = 2
labels = ['u_3']
elif options.transform == 'bend':
ilog = 0
labels = ['u_1']
elif options.transform == 'twist':
ilog = [0, 1, 2]
labels = ['u_1', 'u_2', 'u_3']
label = ', '.join(labels)
log = []
for nx in xrange(*nxs):
shape = (nx, 2)
pb, state, u, gamma2 = solve_problem(shape, dims, young, poisson, force,
transform=options.transform)
dofs = u.get_state_in_region(gamma2)
output('DOFs along the loaded edge:')
output('\n%s' % dofs)
log.append([nx - 1] + nm.array(dofs[0, ilog], ndmin=1).tolist())
pb.save_state(odir('shell10x_cantilever.vtk'), state)
log = nm.array(log)
output('max. %s displacement w.r.t. number of cells:' % label)
output('\n%s' % log)
output('analytical value:', u_exact)
if options.plot:
import matplotlib.pyplot as plt
plt.rcParams.update({
'lines.linewidth' : 3,
'font.size' : 16,
})
fig, ax1 = plt.subplots()
fig.suptitle('max. $%s$ displacement' % label)
for ic in range(log.shape[1] - 1):
ax1.plot(log[:, 0], log[:, ic + 1], label=r'$%s$' % labels[ic])
ax1.set_xlabel('# of cells')
ax1.set_ylabel(r'$%s$' % label)
ax1.grid(which='both')
lines1, labels1 = ax1.get_legend_handles_labels()
if u_exact is not None:
ax1.hlines(u_exact, log[0, 0], log[-1, 0],
'r', 'dotted', label=r'$%s^{analytical}$' % label)
ax2 = ax1.twinx()
# Assume single log column.
ax2.semilogy(log[:, 0], nm.abs(log[:, 1] - u_exact), 'g',
label=r'$|%s - %s^{analytical}|$' % (label, label))
ax2.set_ylabel(r'$|%s - %s^{analytical}|$' % (label, label))
lines2, labels2 = ax2.get_legend_handles_labels()
else:
lines2, labels2 = [], []
ax1.legend(lines1 + lines2, labels1 + labels2, loc='best')
plt.tight_layout()
ax1.set_xlim([log[0, 0] - 2, log[-1, 0] + 2])
suffix = {None: 'straight',
'bend' : 'bent', 'twist' : 'twisted'}[options.transform]
fig.savefig(odir('shell10x_cantilever_convergence_%s.png' % suffix))
plt.show()
if options.show:
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.domain_specific import DomainSpecificPlot
ds = {'u_disp' :
DomainSpecificPlot('plot_displacements',
['rel_scaling=%f' % options.scaling])}
view = Viewer(odir('shell10x_cantilever.vtk'))
view(domain_specific=ds, is_scalar_bar=True, is_wireframe=True,
opacity={'wireframe' : 0.5})
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-n',
'--dry-run',
action='store_true',
dest='dry_run',
default=False,
help=helps['dry_run'])
parser.add_argument('doc_dir')
parser.add_argument('top_dir')
options = parser.parse_args()
doc_dir, top_dir = [
os.path.realpath(ii) for ii in [options.doc_dir, options.top_dir]
]
docs = set(ii for ii in locate_files('*.rst', root_dir=doc_dir))
sources = set(
ii
for ii in locate_files('*.py', root_dir=os.path.join(top_dir, 'sfepy'))
if os.path.basename(ii) not in omits)
sources.update(ii for ii in locate_files(
'*.pyx', root_dir=os.path.join(top_dir, 'sfepy'))
if os.path.basename(ii) not in omits_pyx)
scripts = set(ii for ii in locate_files(
'*.py', root_dir=os.path.join(top_dir, 'script'))
if os.path.basename(ii) not in omits)
top_scripts = set(
os.path.realpath(ii)
for ii in fnmatch.filter(os.listdir(top_dir), '*.py')
if os.path.basename(ii) not in omits)
all_sources = set()
all_sources.update(sources, scripts, top_scripts)
cwd = os.path.realpath(os.path.curdir) + os.path.sep
output.prefix = 'smd:'
output('removing unneeded rst files in "%s"...' % doc_dir)
for doc in sorted(docs):
aux = edit_filename(doc, new_ext='.py')
src1 = os.path.normpath(aux.replace(doc_dir, top_dir))
aux = edit_filename(doc, new_ext='.pyx')
src2 = os.path.normpath(aux.replace(doc_dir, top_dir))
if (src1 not in all_sources) and (src2 not in all_sources):
output('remove: %s' % doc.replace(cwd, ''))
if not options.dry_run:
os.remove(doc)
output('...done')
output('creating missing rst files in "%s"...' % doc_dir)
for src in sorted(all_sources):
aux = edit_filename(src, new_ext='.rst')
doc = os.path.normpath(aux.replace(top_dir, doc_dir))
if doc not in docs:
output('create: %s' % doc.replace(cwd, ''))
if not options.dry_run:
mod_filename = src.replace(top_dir + os.path.sep, '')
mod_name = mod_filename.replace(os.path.sep, '.')
mod_name = edit_filename(mod_name, new_ext='')
if mod_name.startswith('sfepy'): # Module.
title = mod_name + ' module'
else: # Script.
title = mod_filename + ' script'
mod_name = mod_name.split('.')[-1]
underlines = '=' * len(title)
contents = doc_template % (title, underlines, mod_name)
ensure_path(doc)
fd = open(doc, 'w')
fd.write(contents)
fd.close()
output('...done')
def _region_leaf(level, op):
token, details = op['token'], op['orig']
if token != 'KW_Region':
parse_def = token + '<' + ' '.join(details) + '>'
region = Region('leaf', rdef, domain, parse_def=parse_def)
if token == 'KW_Region':
details = details[1][2:]
aux = regions.find(details)
if not aux:
raise ValueError, 'region %s does not exist' % details
else:
if rdef[:4] == 'copy':
region = aux.copy()
else:
region = aux
elif token == 'KW_All':
region.set_vertices(nm.arange(domain.mesh.n_nod, dtype=nm.int32))
elif token == 'E_NIR':
where = details[2]
if where[0] == '[':
out = nm.array(eval(where), dtype=nm.int32)
assert_(nm.amin(out) >= 0)
assert_(nm.amax(out) < domain.mesh.n_nod)
else:
coors = domain.get_mesh_coors()
x = coors[:, 0]
y = coors[:, 1]
if domain.mesh.dim == 3:
z = coors[:, 2]
else:
z = None
coor_dict = {'x': x, 'y': y, 'z': z}
out = nm.where(eval(where, {}, coor_dict))[0]
region.set_vertices(out)
elif token == 'E_NOS':
if domain.fa: # 3D.
fa = domain.fa
else:
fa = domain.ed
flag = fa.mark_surface_facets()
ii = nm.where(flag > 0)[0]
aux = nm.unique(fa.facets[ii])
if aux[0] == -1: # Triangular faces have -1 as 4. point.
aux = aux[1:]
region.can_cells = False
region.set_vertices(aux)
elif token == 'E_NBF':
where = details[2]
coors = domain.get_mesh_coors()
fun = functions[where]
out = fun(coors, domain=domain)
region.set_vertices(out)
elif token == 'E_EBF':
where = details[2]
coors = domain.get_mesh_coors()
fun = functions[where]
out = fun(coors, domain=domain)
region.set_cells(out)
elif token == 'E_EOG':
group = int(details[3])
ig = domain.mat_ids_to_i_gs[group]
group = domain.groups[ig]
region.set_from_group(ig, group.vertices, group.shape.n_el)
elif token == 'E_NOG':
try:
group = int(details[3])
group_nodes = nm.where(domain.mesh.ngroups == group)[0]
except ValueError:
try:
group_nodes = domain.mesh.nodal_bcs[details[3]]
except KeyError:
msg = 'undefined nodal group! (%s)' % details[3]
raise ValueError(msg)
region.set_vertices(group_nodes)
elif token == 'E_ONIR':
aux = regions[details[3][2:]]
region.set_vertices(aux.all_vertices[0:1])
elif token == 'E_NI':
region.set_vertices(
nm.array([int(ii) for ii in details[1:]], dtype=nm.int32))
elif token == 'E_EI1':
region.set_cells(
{0: nm.array([int(ii) for ii in details[1:]], dtype=nm.int32)})
elif token == 'E_EI2':
num = len(details[1:]) / 2
cells = {}
for ii in range(num):
ig, iel = int(details[1 + 2 * ii]), int(details[2 + 2 * ii])
cells.setdefault(ig, []).append(iel)
region.set_cells(cells)
else:
output('token "%s" unkown - check regions!' % token)
raise NotImplementedError
return region
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars',
metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store',
dest='pars',
default=default_pars,
help=helps['pars'])
parser.add_argument('--conf',
metavar='filename',
action='store',
dest='conf',
default=None,
help=helps['conf'])
parser.add_argument('--mesh-size',
type=float,
metavar='float',
action='store',
dest='mesh_size',
default=None,
help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store',
dest='unit_multipliers',
default='1.0,1.0,1.0',
help=helps['unit_multipliers'])
parser.add_argument('--plane',
action='store',
dest='plane',
choices=['strain', 'stress'],
default='strain',
help=helps['plane'])
parser.add_argument('--wave-dir',
metavar='float,float[,float]',
action='store',
dest='wave_dir',
default='1.0,0.0,0.0',
help=helps['wave_dir'])
parser.add_argument('--mode',
action='store',
dest='mode',
choices=['omega', 'kappa'],
default='omega',
help=helps['mode'])
parser.add_argument('--range',
metavar='start,stop,count',
action='store',
dest='range',
default='0,6.4,33',
help=helps['range'])
parser.add_argument('--order',
metavar='int',
type=int,
action='store',
dest='order',
default=1,
help=helps['order'])
parser.add_argument('--refine',
metavar='int',
type=int,
action='store',
dest='refine',
default=0,
help=helps['refine'])
parser.add_argument('-n',
'--n-eigs',
metavar='int',
type=int,
action='store',
dest='n_eigs',
default=6,
help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true',
dest='eigs_only',
default=False,
help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true',
dest='post_process',
default=False,
help=helps['post_process'])
parser.add_argument('--solver-conf',
metavar='dict-like',
action='store',
dest='solver_conf',
default=default_solver_conf,
help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true',
dest='save_regions',
default=False,
help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true',
dest='save_materials',
default=False,
help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true',
dest='log_std_waves',
default=False,
help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false',
dest='show_legends',
default=True,
help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false',
dest='show',
default=True,
help=helps['no_show'])
parser.add_argument('--silent',
action='store_true',
dest='silent',
default=False,
help=helps['silent'])
parser.add_argument('-c',
'--clear',
action='store_true',
dest='clear',
default=False,
help=helps['clear'])
parser.add_argument('-o',
'--output-dir',
metavar='path',
action='store',
dest='output_dir',
default='output',
help=helps['output_dir'])
parser.add_argument('mesh_filename',
default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir, 'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [
float(ii) for ii in options.unit_multipliers.split(',')
]
options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
if options.clear:
remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
output('material parameters with applied unit multipliers:')
output(pars)
if options.mode == 'omega':
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['wave_number', 'wave_number'],
options.unit_multipliers)
output('wave number range with applied unit multipliers:', rng)
else:
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['frequency', 'frequency'],
options.unit_multipliers)
output('frequency range with applied unit multipliers:', rng)
pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir,
options)
dim = pb.domain.shape.dim
if dim != 2:
options.plane = 'strain'
if options.save_regions:
pb.save_regions_as_groups(os.path.join(output_dir, 'regions'))
if options.save_materials:
save_materials(output_dir, pb, options)
conf = pb.solver_confs['eig']
eig_solver = Solver.any_from_conf(conf)
n_eigs, options.n_eigs = setup_n_eigs(options, pb, mtxs)
get_color = lambda ii: plt.cm.viridis((float(ii) / (options.n_eigs - 1)))
plot_kwargs = [{
'color': get_color(ii),
'ls': '',
'marker': 'o'
} for ii in range(options.n_eigs)]
log_names = []
log_plot_kwargs = []
if options.log_std_waves:
std_wave_fun, log_names, log_plot_kwargs = get_std_wave_fun(
pb, options)
else:
std_wave_fun = None
stepper = get_stepper(rng, pb, options)
if options.mode == 'omega':
eigenshapes_filename = os.path.join(
output_dir, 'frequency-eigenshapes-%s.vtk' % stepper.suffix)
log = Log(
[[r'$\lambda_{%d}$' % ii for ii in range(options.n_eigs)],
[r'$\omega_{%d}$' % ii
for ii in range(options.n_eigs)] + log_names],
plot_kwargs=[plot_kwargs, plot_kwargs + log_plot_kwargs],
formats=[['{:.5e}'] * options.n_eigs,
['{:.5e}'] * (options.n_eigs + len(log_names))],
yscales=['linear', 'linear'],
xlabels=[r'$\kappa$', r'$\kappa$'],
ylabels=[r'eigenvalues $\lambda_i$', r'frequencies $\omega_i$'],
show_legends=options.show_legends,
is_plot=options.show,
log_filename=os.path.join(output_dir, 'frequencies.txt'),
aggregate=1000,
sleep=0.1)
for iv, wmag in stepper:
output('step %d: wave vector %s' % (iv, wmag * wdir))
evp_mtxs = build_evp_matrices(mtxs, wmag, options.mode, pb)
if options.eigs_only:
eigs = eig_solver(*evp_mtxs, n_eigs=n_eigs, eigenvectors=False)
svecs = None
else:
eigs, svecs = eig_solver(*evp_mtxs,
n_eigs=n_eigs,
eigenvectors=True)
omegas, svecs, out = process_evp_results(eigs,
svecs,
wmag,
options.mode,
wdir,
bzone,
pb,
mtxs,
std_wave_fun=std_wave_fun)
log(*out, x=[wmag, wmag])
save_eigenvectors(eigenshapes_filename % iv, svecs, wmag, wdir, pb)
gc.collect()
log(save_figure=os.path.join(output_dir, 'frequencies.png'))
log(finished=True)
else:
eigenshapes_filename = os.path.join(
output_dir, 'wave-number-eigenshapes-%s.vtk' % stepper.suffix)
log = Log([[r'$\kappa_{%d}$' % ii
for ii in range(options.n_eigs)] + log_names],
plot_kwargs=[plot_kwargs + log_plot_kwargs],
formats=[['{:.5e}'] * (options.n_eigs + len(log_names))],
yscales=['linear'],
xlabels=[r'$\omega$'],
ylabels=[r'wave numbers $\kappa_i$'],
show_legends=options.show_legends,
is_plot=options.show,
log_filename=os.path.join(output_dir, 'wave-numbers.txt'),
aggregate=1000,
sleep=0.1)
for io, omega in stepper:
output('step %d: frequency %s' % (io, omega))
evp_mtxs = build_evp_matrices(mtxs, omega, options.mode, pb)
if options.eigs_only:
eigs = eig_solver(*evp_mtxs, n_eigs=n_eigs, eigenvectors=False)
svecs = None
else:
eigs, svecs = eig_solver(*evp_mtxs,
n_eigs=n_eigs,
eigenvectors=True)
kappas, svecs, out = process_evp_results(eigs,
svecs,
omega,
options.mode,
wdir,
bzone,
pb,
mtxs,
std_wave_fun=std_wave_fun)
log(*out, x=[omega])
save_eigenvectors(eigenshapes_filename % io, svecs, kappas, wdir,
pb)
gc.collect()
log(save_figure=os.path.join(output_dir, 'wave-numbers.png'))
log(finished=True)
def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('--young',
metavar='float',
type=float,
action='store',
dest='young',
default=2000.0,
help=helps['young'])
parser.add_option('--poisson',
metavar='float',
type=float,
action='store',
dest='poisson',
default=0.4,
help=helps['poisson'])
parser.add_option('--load',
metavar='float',
type=float,
action='store',
dest='load',
default=-1000.0,
help=helps['load'])
parser.add_option('--order',
metavar='int',
type=int,
action='store',
dest='order',
default=1,
help=helps['order'])
parser.add_option('-r',
'--refine',
metavar='int',
type=int,
action='store',
dest='refine',
default=0,
help=helps['refine'])
parser.add_option('-s',
'--show',
action="store_true",
dest='show',
default=False,
help=helps['show'])
parser.add_option('-p',
'--probe',
action="store_true",
dest='probe',
default=False,
help=helps['probe'])
options, args = parser.parse_args()
assert_((0.0 < options.poisson < 0.5),
"Poisson's ratio must be in ]0, 0.5[!")
assert_((0 < options.order),
'displacement approximation order must be at least 1!')
output('using values:')
output(" Young's modulus:", options.young)
output(" Poisson's ratio:", options.poisson)
output(' vertical load:', options.load)
output('uniform mesh refinement level:', options.refine)
# Build the problem definition.
mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.mesh')
domain = FEDomain('domain', mesh)
if options.refine > 0:
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements' %
(domain.shape.n_nod, domain.shape.n_el))
omega = domain.create_region('Omega', 'all')
left = domain.create_region('Left', 'vertices in x < 0.001', 'facet')
bottom = domain.create_region('Bottom', 'vertices in y < 0.001', 'facet')
top = domain.create_region('Top', 'vertex 2', 'vertex')
field = Field.from_args('fu',
nm.float64,
'vector',
omega,
approx_order=options.order)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
D = stiffness_from_youngpoisson(2, options.young, options.poisson)
asphalt = Material('Asphalt', D=D)
load = Material('Load', values={'.val': [0.0, options.load]})
integral = Integral('i', order=2 * options.order)
integral0 = Integral('i', order=0)
t1 = Term.new('dw_lin_elastic(Asphalt.D, v, u)',
integral,
omega,
Asphalt=asphalt,
v=v,
u=u)
t2 = Term.new('dw_point_load(Load.val, v)', integral0, top, Load=load, v=v)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
xsym = EssentialBC('XSym', bottom, {'u.1': 0.0})
ysym = EssentialBC('YSym', left, {'u.0': 0.0})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
pb.time_update(ebcs=Conditions([xsym, ysym]))
# Solve the problem.
state = pb.solve()
output(nls_status)
# Postprocess the solution.
out = state.create_output_dict()
out = stress_strain(out, pb, state, extend=True)
pb.save_state('its2D_interactive.vtk', out=out)
gdata = geometry_data['2_3']
nc = len(gdata.coors)
integral_vn = Integral('ivn',
coors=gdata.coors,
weights=[gdata.volume / nc] * nc)
nodal_stress(out, pb, state, integrals=Integrals([integral_vn]))
if options.probe:
# Probe the solution.
probes, labels = gen_lines(pb)
sfield = Field.from_args('sym_tensor',
nm.float64,
3,
omega,
approx_order=options.order - 1)
stress = FieldVariable('stress',
'parameter',
sfield,
primary_var_name='(set-to-None)')
strain = FieldVariable('strain',
'parameter',
sfield,
primary_var_name='(set-to-None)')
cfield = Field.from_args('component',
nm.float64,
1,
omega,
approx_order=options.order - 1)
component = FieldVariable('component',
'parameter',
cfield,
primary_var_name='(set-to-None)')
ev = pb.evaluate
order = 2 * (options.order - 1)
strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp')
stress_qp = ev('ev_cauchy_stress.%d.Omega(Asphalt.D, u)' % order,
mode='qp',
copy_materials=False)
project_by_component(strain, strain_qp, component, order)
project_by_component(stress, stress_qp, component, order)
all_results = []
for ii, probe in enumerate(probes):
fig, results = probe_results(u, strain, stress, probe, labels[ii])
fig.savefig('its2D_interactive_probe_%d.png' % ii)
all_results.append(results)
for ii, results in enumerate(all_results):
output('probe %d:' % ii)
output.level += 2
for key, res in ordered_iteritems(results):
output(key + ':')
val = res[1]
output(' min: %+.2e, mean: %+.2e, max: %+.2e' %
(val.min(), val.mean(), val.max()))
output.level -= 2
if options.show:
# Show the solution. If the approximation order is greater than 1, the
# extra DOFs are simply thrown away.
from sfepy.postprocess.viewer import Viewer
view = Viewer('its2D_interactive.vtk')
view(vector_mode='warp_norm',
rel_scaling=1,
is_scalar_bar=True,
is_wireframe=True)
def __call__(self,
mtx_m,
mtx_d,
mtx_k,
n_eigs=None,
eigenvectors=None,
status=None,
conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k], [mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None], [None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = max_diff_csr(mtx_m, mtx_l * mtx_l.T)
mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64)
mtx_a = sps.bmat([[-mtx_k, None], [None, mtx_eye]])
mtx_b = sps.bmat([[mtx_d, mtx_l], [mtx_l.T, None]])
else:
raise ValueError('unknown method! (%s)' % conf.method)
if conf.debug:
ssym['|A - A^T|'] = max_diff_csr(mtx_a, mtx_a.T)
ssym['|A - A^H|'] = max_diff_csr(mtx_a, mtx_a.H)
ssym['|B - B^T|'] = max_diff_csr(mtx_b, mtx_b.T)
ssym['|B - B^H|'] = max_diff_csr(mtx_b, mtx_b.H)
for key, val in sorted(ssym.items()):
output('{}: {}'.format(key, val))
if conf.mode == 'normal':
out = self.solver(mtx_a,
mtx_b,
n_eigs=n_eigs,
eigenvectors=eigenvectors,
status=status)
if eigenvectors:
eigs, vecs = out
out = (eigs, vecs[:mtx_m.shape[0], :])
if conf.debug:
res = mtx_a.dot(vecs) - eigs * mtx_b.dot(vecs)
status['lin. error'] = nm.linalg.norm(res, nm.inf)
else:
out = self.solver(mtx_b,
mtx_a,
n_eigs=n_eigs,
eigenvectors=eigenvectors,
status=status)
if eigenvectors:
eigs, vecs = out
out = (1.0 / eigs, vecs[:mtx_m.shape[0], :])
if conf.debug:
res = (1.0 / eigs) * mtx_b.dot(vecs) - mtx_a.dot(vecs)
status['lin. error'] = nm.linalg.norm(res, nm.inf)
else:
out = 1.0 / out
if conf.debug and eigenvectors:
eigs, vecs = out
res = ((eigs**2 * (mtx_m.dot(vecs))) + (eigs * (mtx_d.dot(vecs))) +
(mtx_k.dot(vecs)))
status['error'] = nm.linalg.norm(res, nm.inf)
return out
def main():
parser = ArgumentParser(description=__doc__)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-b',
'--basis',
metavar='name',
action='store',
dest='basis',
default='lagrange',
help=helps['basis'])
parser.add_argument('-n',
'--max-order',
metavar='order',
type=int,
action='store',
dest='max_order',
default=10,
help=helps['max_order'])
parser.add_argument('-m',
'--matrix',
action='store',
dest='matrix_type',
choices=['laplace', 'elasticity', 'smass', 'vmass'],
default='laplace',
help=helps['matrix_type'])
parser.add_argument('-g',
'--geometry',
metavar='name',
action='store',
dest='geometry',
default='2_4',
help=helps['geometry'])
parser.add_argument('-o',
'--output-dir',
metavar='path',
action='store',
dest='output_dir',
default=None,
help=helps['output_dir'])
parser.add_argument('--no-show',
action='store_false',
dest='show',
default=True,
help=helps['no_show'])
options = parser.parse_args()
dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
output('reference element geometry:')
output(' dimension: %d, vertices: %d' % (dim, n_ep))
n_c = {
'laplace': 1,
'elasticity': dim,
'smass': 1,
'vmass': dim
}[options.matrix_type]
output('matrix type:', options.matrix_type)
output('number of variable components:', n_c)
output('polynomial space:', options.basis)
output('max. order:', options.max_order)
mesh = Mesh.from_file(data_dir +
'/meshes/elements/%s_1.mesh' % options.geometry)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
orders = nm.arange(1, options.max_order + 1, dtype=nm.int32)
conds = []
for order in orders:
output('order:', order, '...')
field = Field.from_args('fu',
nm.float64,
n_c,
omega,
approx_order=order,
space='H1',
poly_space_base=options.basis)
quad_order = 2 * field.approx_order
output('quadrature order:', quad_order)
integral = Integral('i', order=quad_order)
qp, _ = integral.get_qp(options.geometry)
output('number of quadrature points:', qp.shape[0])
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = Material('m', D=stiffness_from_lame(dim, 1.0, 1.0))
if options.matrix_type == 'laplace':
term = Term.new('dw_laplace(v, u)', integral, omega, v=v, u=u)
n_zero = 1
elif options.matrix_type == 'elasticity':
term = Term.new('dw_lin_elastic(m.D, v, u)',
integral,
omega,
m=m,
v=v,
u=u)
n_zero = (dim + 1) * dim // 2
elif options.matrix_type in ('smass', 'vmass'):
term = Term.new('dw_dot(v, u)', integral, omega, v=v, u=u)
n_zero = 0
term.setup()
output('assembling...')
timer = Timer(start=True)
mtx, iels = term.evaluate(mode='weak', diff_var='u')
output('...done in %.2f s' % timer.stop())
mtx = mtx[0, 0]
try:
assert_(nm.max(nm.abs(mtx - mtx.T)) < 1e-10)
except:
from sfepy.base.base import debug
debug()
output('matrix shape:', mtx.shape)
eigs = eig(mtx, method='eig.sgscipy', eigenvectors=False)
eigs.sort()
# Zero 'true' zeros.
eigs[:n_zero] = 0.0
ii = nm.where(eigs < 0.0)[0]
if len(ii):
output('matrix is not positive semi-definite!')
ii = nm.where(eigs[n_zero:] < 1e-12)[0]
if len(ii):
output('matrix has more than %d zero eigenvalues!' % n_zero)
output('smallest eigs:\n', eigs[:10])
ii = nm.where(eigs > 0.0)[0]
emin, emax = eigs[ii[[0, -1]]]
output('min:', emin, 'max:', emax)
cond = emax / emin
conds.append(cond)
output('condition number:', cond)
output('...done')
if options.output_dir is not None:
indir = partial(op.join, options.output_dir)
else:
indir = None
plt.rcParams['font.size'] = 12
plt.rcParams['lines.linewidth'] = 3
fig, ax = plt.subplots()
ax.semilogy(orders, conds)
ax.set_xticks(orders)
ax.set_xticklabels(orders)
ax.set_xlabel('polynomial order')
ax.set_ylabel('condition number')
ax.set_title(f'{options.basis.capitalize()} basis')
ax.grid()
plt.tight_layout()
if indir is not None:
fig.savefig(indir(f'{options.basis}-{options.matrix_type}-'
f'{options.geometry}-{options.max_order}-xlin.png'),
bbox_inches='tight')
fig, ax = plt.subplots()
ax.loglog(orders, conds)
ax.set_xticks(orders)
ax.set_xticklabels(orders)
ax.set_xlabel('polynomial order')
ax.set_ylabel('condition number')
ax.set_title(f'{options.basis.capitalize()} basis')
ax.grid()
plt.tight_layout()
if indir is not None:
fig.savefig(indir(f'{options.basis}-{options.matrix_type}-'
f'{options.geometry}-{options.max_order}-xlog.png'),
bbox_inches='tight')
if options.show:
plt.show()
def get_ref_coors(field,
coors,
strategy='kdtree',
close_limit=0.1,
cache=None,
verbose=True):
"""
Get reference element coordinates and elements corresponding to given
physical coordinates.
Parameters
----------
field : Field instance
The field defining the approximation.
coors : array
The physical coordinates.
strategy : str, optional
The strategy for finding the elements that contain the
coordinates. Only 'kdtree' is supported for the moment.
close_limit : float, optional
The maximum limit distance of a point from the closest
element allowed for extrapolation.
cache : Struct, optional
To speed up a sequence of evaluations, the field mesh, the inverse
connectivity of the field mesh and the KDTree instance can be cached as
`cache.mesh`, `cache.offsets`, `cache.iconn` and
`cache.kdtree`. Optionally, the cache can also contain the reference
element coordinates as `cache.ref_coors`, `cache.cells` and
`cache.status`, if the evaluation occurs in the same coordinates
repeatedly. In that case the KDTree related data are ignored.
verbose : bool
If False, reduce verbosity.
Returns
-------
ref_coors : array
The reference coordinates.
cells : array
The cell indices corresponding to the reference coordinates.
status : array
The status: 0 is success, 1 is extrapolation within `close_limit`, 2 is
extrapolation outside `close_limit`, 3 is failure.
"""
ref_coors = get_default_attr(cache, 'ref_coors', None)
if ref_coors is None:
mesh = get_default_attr(cache, 'mesh', None)
if mesh is None:
mesh = field.create_mesh(extra_nodes=False)
scoors = mesh.coors
output('reference field: %d vertices' % scoors.shape[0],
verbose=verbose)
iconn = get_default_attr(cache, 'iconn', None)
if iconn is None:
offsets, iconn = make_inverse_connectivity(mesh.conns,
mesh.n_nod,
ret_offsets=True)
ii = nm.where(offsets[1:] == offsets[:-1])[0]
if len(ii):
raise ValueError('some vertices not in any element! (%s)' % ii)
else:
offsets = cache.offsets
if strategy == 'kdtree':
kdtree = get_default_attr(cache, 'kdtree', None)
if kdtree is None:
from scipy.spatial import cKDTree as KDTree
tt = time.clock()
kdtree = KDTree(scoors)
output('kdtree: %f s' % (time.clock() - tt), verbose=verbose)
tt = time.clock()
ics = kdtree.query(coors)[1]
output('kdtree query: %f s' % (time.clock() - tt), verbose=verbose)
tt = time.clock()
ics = nm.asarray(ics, dtype=nm.int32)
vertex_coorss, nodess, mtx_is = [], [], []
conns = []
for ig, ap in field.aps.iteritems():
ps = ap.interp.gel.interp.poly_spaces['v']
vertex_coorss.append(ps.geometry.coors)
nodess.append(ps.nodes)
mtx_is.append(ps.get_mtx_i())
conns.append(mesh.conns[ig].copy())
# Get reference element coordinates corresponding to
# destination coordinates.
ref_coors = nm.empty_like(coors)
cells = nm.empty((coors.shape[0], 2), dtype=nm.int32)
status = nm.empty((coors.shape[0], ), dtype=nm.int32)
find_ref_coors(ref_coors, cells, status, coors, ics, offsets,
iconn, scoors, conns, vertex_coorss, nodess, mtx_is,
1, close_limit, 1e-15, 100, 1e-8)
output('ref. coordinates: %f s' % (time.clock() - tt),
verbose=verbose)
elif strategy == 'crawl':
raise NotImplementedError
else:
raise ValueError('unknown search strategy! (%s)' % strategy)
else:
ref_coors = cache.ref_coors
cells = cache.cells
status = cache.status
return ref_coors, cells, status
def assemble_matrices(define, mod, pars, set_wave_dir, options):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_problem = functools.partial(define,
filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process)
conf = ProblemConf.from_dict(define_problem(), mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def get_evaluate_cache(self,
cache=None,
share_geometry=False,
verbose=False):
"""
Get the evaluate cache for :func:`Variable.evaluate_at()
<sfepy.discrete.variables.Variable.evaluate_at()>`.
Parameters
----------
cache : Struct instance, optional
Optionally, use the provided instance to store the cache data.
share_geometry : bool
Set to True to indicate that all the evaluations will work on the
same region. Certain data are then computed only for the first
probe and cached.
verbose : bool
If False, reduce verbosity.
Returns
-------
cache : Struct instance
The evaluate cache.
"""
import time
try:
from scipy.spatial import cKDTree as KDTree
except ImportError:
from scipy.spatial import KDTree
from sfepy.discrete.fem.geometry_element import create_geometry_elements
if cache is None:
cache = Struct(name='evaluate_cache')
tt = time.clock()
if (cache.get('cmesh', None) is None) or not share_geometry:
mesh = self.create_mesh(extra_nodes=False)
cache.cmesh = cmesh = mesh.cmesh
gels = create_geometry_elements()
cmesh.set_local_entities(gels)
cmesh.setup_entities()
cache.centroids = cmesh.get_centroids(cmesh.tdim)
if self.gel.name != '3_8':
cache.normals0 = cmesh.get_facet_normals()
cache.normals1 = None
else:
cache.normals0 = cmesh.get_facet_normals(0)
cache.normals1 = cmesh.get_facet_normals(1)
output('cmesh setup: %f s' % (time.clock() - tt), verbose=verbose)
tt = time.clock()
if (cache.get('kdtree', None) is None) or not share_geometry:
cache.kdtree = KDTree(cmesh.coors)
output('kdtree: %f s' % (time.clock() - tt), verbose=verbose)
return cache
def generate_images(images_dir, examples_dir):
"""
Generate images from results of running examples found in
`examples_dir` directory.
The generated images are stored to `images_dir`,
"""
from sfepy.applications import solve_pde
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.utils import mlab
prefix = output.prefix
output_dir = tempfile.mkdtemp()
trunk = os.path.join(output_dir, 'result')
options = Struct(output_filename_trunk=trunk,
output_format='vtk',
save_ebc=False,
save_ebc_nodes=False,
save_regions=False,
save_field_meshes=False,
save_regions_as_groups=False,
solve_not=False)
default_views = {'': {}}
ensure_path(images_dir + os.path.sep)
view = Viewer('', offscreen=False)
for ex_filename in locate_files('*.py', examples_dir):
if _omit(ex_filename): continue
output.level = 0
output.prefix = prefix
ebase = ex_filename.replace(examples_dir, '')[1:]
output('trying "%s"...' % ebase)
try:
problem, state = solve_pde(ex_filename, options=options)
except KeyboardInterrupt:
raise
except:
problem = None
output('***** failed! *****')
if problem is not None:
if ebase in custom:
views = custom[ebase]
else:
views = default_views
tsolver = problem.get_time_solver()
if tsolver.ts is None:
suffix = None
else:
suffix = tsolver.ts.suffix % (tsolver.ts.n_step - 1)
filename = problem.get_output_name(suffix=suffix)
for suffix, kwargs in six.iteritems(views):
fig_filename = _get_fig_filename(ebase, images_dir, suffix)
fname = edit_filename(filename, suffix=suffix)
output('displaying results from "%s"' % fname)
disp_name = fig_filename.replace(sfepy.data_dir, '')
output('to "%s"...' % disp_name.lstrip(os.path.sep))
view.filename = fname
view(scene=view.scene,
show=False,
is_scalar_bar=True,
**kwargs)
view.save_image(fig_filename)
mlab.clf()
output('...done')
remove_files(output_dir)
output('...done')
def generate_rst_files(rst_dir, examples_dir, images_dir):
"""
Generate Sphinx rst files for examples in `examples_dir` with images
in `images_dir` and put them into `rst_dir`.
Returns
-------
dir_map : dict
The directory mapping of examples and corresponding rst files.
"""
ensure_path(rst_dir + os.path.sep)
output('generating rst files...')
dir_map = {}
for ex_filename in locate_files('*.py', examples_dir):
if _omit(ex_filename): continue
ebase = ex_filename.replace(examples_dir, '')[1:]
base_dir = os.path.dirname(ebase)
rst_filename = os.path.basename(ex_filename).replace('.py', '.rst')
dir_map.setdefault(base_dir, []).append((ex_filename, rst_filename))
for dirname, filenames in six.iteritems(dir_map):
filenames = sorted(filenames, key=lambda a: a[1])
dir_map[dirname] = filenames
# Main index.
mfd = open(os.path.join(rst_dir, 'index.rst'), 'w')
mfd.write(_index % ('sfepy', 'Examples', '=' * 8))
for dirname, filenames in ordered_iteritems(dir_map):
full_dirname = os.path.join(rst_dir, dirname)
ensure_path(full_dirname + os.path.sep)
# Subdirectory index.
ifd = open(os.path.join(full_dirname, 'index.rst'), 'w')
ifd.write(_index % (dirname, dirname, '=' * len(dirname)))
for ex_filename, rst_filename in filenames:
full_rst_filename = os.path.join(full_dirname, rst_filename)
output('"%s"' % full_rst_filename.replace(rst_dir, '')[1:])
rst_filename_ns = rst_filename.replace('.rst', '')
ebase = ex_filename.replace(examples_dir, '')[1:]
rst_ex_filename = _make_sphinx_path(ex_filename)
docstring = get_default(
import_file(ex_filename).__doc__, 'missing description!')
ifd.write(' %s\n' % rst_filename_ns)
fig_include = ''
fig_base = _get_fig_filenames(ebase, images_dir).next()
for fig_filename in _get_fig_filenames(ebase, images_dir):
rst_fig_filename = _make_sphinx_path(fig_filename)
if os.path.exists(fig_filename):
fig_include += _image % rst_fig_filename + '\n'
# Example rst file.
fd = open(full_rst_filename, 'w')
fd.write(_include %
(fig_base, ebase, '=' * len(ebase), docstring,
fig_include, rst_ex_filename, rst_ex_filename))
fd.close()
ifd.close()
mfd.write(' %s/index\n' % dirname)
mfd.close()
output('...done')
return dir_map
def generate_gallery_html(examples_dir, output_filename, gallery_dir, rst_dir,
thumbnails_dir, dir_map, link_prefix):
"""
Generate the gallery html file with thumbnail images and links to
examples.
Parameters
----------
output_filename : str
The output html file name.
gallery_dir : str
The top level directory of gallery files.
rst_dir : str
The full path to rst files of examples within `gallery_dir`.
thumbnails_dir : str
The full path to thumbnail images within `gallery_dir`.
dir_map : dict
The directory mapping returned by `generate_rst_files()`
link_prefix : str, optional
The prefix to prepend to links to individual pages of examples.
"""
output('generating %s...' % output_filename)
with open(_gallery_template_file, 'r') as fd:
gallery_template = fd.read()
div_lines = []
sidebar = []
for dirname, filenames in ordered_iteritems(dir_map):
full_dirname = os.path.join(rst_dir, dirname)
dirnamenew = dirname.replace("_", " ")
sidebarline = _side_links % (dirname, dirnamenew.title())
lines = []
for ex_filename, rst_filename in filenames:
full_rst_filename = os.path.join(full_dirname, rst_filename)
ebase = full_rst_filename.replace(rst_dir, '')[1:]
ebase = edit_filename(ebase, new_ext='.py')
link_base = full_rst_filename.replace(gallery_dir, '')[1:]
link = os.path.join(link_prefix,
os.path.splitext(link_base)[0] + '.html')
_get_fig_filenames(ebase, thumbnails_dir).next()
for thumbnail_filename in _get_fig_filenames(
ebase, thumbnails_dir):
if not os.path.isfile(thumbnail_filename):
# Skip examples with no image (= failed examples).
continue
thumbnail_name = thumbnail_filename.replace(gallery_dir,
'')[1:]
path_to_file = os.path.join(examples_dir, ebase)
docstring = get_default(
import_file(path_to_file).__doc__, 'missing description!')
docstring = docstring.replace('e.g.', 'eg:')
docstring = docstring.split('.')
line = _link_template % (link, os.path.splitext(ebase)[0],
thumbnail_name, link,
docstring[0] + '.')
lines.append(line)
if (len(lines) != 0):
div_lines.append(
_div_line %
(dirname, dirnamenew.title(), dirname, '\n'.join(lines)))
sidebar.append(sidebarline)
fd = open(output_filename, 'w')
fd.write(gallery_template % ((link_prefix, ) * 7 +
('\n'.join(sidebar), '\n'.join(div_lines))))
fd.close()
output('...done')
def adapt_time_step(ts, status, adt, problem=None):
"""
Adapt the time step of `ts` according to the exit status of the
nonlinear solver.
The time step dt is reduced, if the nonlinear solver did not converge. If it
converged in less then a specified number of iterations for several time
steps, the time step is increased. This is governed by the following
parameters:
- red_factor : time step reduction factor
- red_max : maximum time step reduction factor
- inc_factor : time step increase factor
- inc_on_iter : increase time step if the nonlinear solver converged in
less than this amount of iterations...
- inc_wait : ...for this number of consecutive time steps
Parameters
----------
ts : VariableTimeStepper instance
The time stepper.
status : IndexedStruct instance
The nonlinear solver exit status.
adt : Struct instance
The adaptivity parameters of the time solver:
problem : Problem instance, optional
This canbe used in user-defined adaptivity functions. Not used here.
Returns
-------
is_break : bool
If True, the adaptivity loop should stop.
"""
is_break = False
if status.condition == 0:
if status.n_iter <= adt.inc_on_iter:
adt.wait += 1
if adt.wait > adt.inc_wait:
if adt.red < 1.0:
adt.red = adt.red * adt.inc_factor
ts.set_time_step(adt.dt0 * adt.red)
output('+++++ new time step: %e +++++' % ts.dt)
adt.wait = 0
else:
adt.wait = 0
is_break = True
else:
adt.red = adt.red * adt.red_factor
if adt.red < adt.red_max:
is_break = True
else:
ts.set_time_step(adt.dt0 * adt.red, update_time=True)
output('----- new time step: %e -----' % ts.dt)
adt.wait = 0
return is_break
def __call__(self,
rhs,
x0=None,
conf=None,
eps_a=None,
eps_r=None,
i_max=None,
mtx=None,
status=None,
context=None,
**kwargs):
solver_kwargs = self.build_solver_kwargs(conf)
eps_r = get_default(eps_r, self.conf.eps_r)
i_max = get_default(i_max, self.conf.i_max)
setup_precond = get_default(kwargs.get('setup_precond', None),
self.conf.setup_precond)
callback = get_default(kwargs.get('callback', lambda sol: None),
self.conf.callback)
self.iter = 0
def iter_callback(sol):
self.iter += 1
msg = '%s: iteration %d' % (self.conf.name, self.iter)
if conf.verbose > 2:
if conf.method not in self._callbacks_res:
res = mtx * sol - rhs
else:
res = sol
rnorm = nm.linalg.norm(res)
msg += ': |Ax-b| = %e' % rnorm
output(msg, verbose=conf.verbose > 1)
# Call an optional user-defined callback.
callback(sol)
precond = setup_precond(mtx, context)
if conf.method == 'qmr':
prec_args = {'M1': precond, 'M2': precond}
else:
prec_args = {'M': precond}
solver_kwargs.update(prec_args)
try:
sol, info = self.solver(mtx,
rhs,
x0=x0,
atol=eps_a,
rtol=eps_r,
maxiter=i_max,
callback=iter_callback,
**solver_kwargs)
except TypeError:
sol, info = self.solver(mtx,
rhs,
x0=x0,
tol=eps_r,
maxiter=i_max,
callback=iter_callback,
**solver_kwargs)
output('%s: %s convergence: %s (%s, %d iterations)' %
(self.conf.name, self.conf.method, info,
self.converged_reasons[nm.sign(info)], self.iter),
verbose=conf.verbose)
return sol, self.iter
