def test_interpolation_two_meshes(self):
from sfepy import data_dir
from sfepy.fem import Mesh, Domain, H1NodalVolumeField, Variables
m1 = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')
m2 = Mesh('target mesh',
data_dir + '/meshes/3d/cube_medium_tetra.mesh')
m2.coors *= 2.0
bbox = m1.get_bounding_box()
dd = bbox[1, :] - bbox[0, :]
data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])
variables1 = {
'u': ('unknown field', 'scalar_tp', 0),
'v': ('test field', 'scalar_tp', 'u'),
}
variables2 = {
'u': ('unknown field', 'scalar_si', 0),
'v': ('test field', 'scalar_si', 'u'),
}
d1 = Domain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
field1 = H1NodalVolumeField('scalar_tp',
nm.float64, (1, 1),
omega1,
approx_order=1)
ff1 = {field1.name: field1}
d2 = Domain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = H1NodalVolumeField('scalar_si',
nm.float64, (1, 1),
omega2,
approx_order=0)
ff2 = {field2.name: field2}
vv1 = Variables.from_conf(transform_variables(variables1), ff1)
u1 = vv1['u']
u1.set_from_mesh_vertices(data)
vv2 = Variables.from_conf(transform_variables(variables2), ff2)
u2 = vv2['u']
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)
fname = in_dir(self.options.out_dir)
u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))
return True
def test_interpolation_two_meshes(self):
from sfepy import data_dir
from sfepy.fem import Mesh, Domain, H1NodalVolumeField, Variables
m1 = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')
m2 = Mesh('target mesh', data_dir + '/meshes/3d/cube_medium_tetra.mesh')
m2.coors *= 2.0
bbox = m1.get_bounding_box()
dd = bbox[1,:] - bbox[0,:]
data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])
variables1 = {
'u' : ('unknown field', 'scalar_tp', 0),
'v' : ('test field', 'scalar_tp', 'u'),
}
variables2 = {
'u' : ('unknown field', 'scalar_si', 0),
'v' : ('test field', 'scalar_si', 'u'),
}
d1 = Domain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
field1 = H1NodalVolumeField('scalar_tp', nm.float64, (1,1), omega1,
approx_order=1)
ff1 = {field1.name : field1}
d2 = Domain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = H1NodalVolumeField('scalar_si', nm.float64, (1,1), omega2,
approx_order=0)
ff2 = {field2.name : field2}
vv1 = Variables.from_conf(transform_variables(variables1), ff1)
u1 = vv1['u']
u1.set_from_mesh_vertices(data)
vv2 = Variables.from_conf(transform_variables(variables2), ff2)
u2 = vv2['u']
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)
fname = in_dir(self.options.out_dir)
u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))
return True
def do_interpolation(m2, m1, data, field_name, force=False):
"""Interpolate data from m1 to m2. """
from sfepy.fem import Domain, H1NodalVolumeField, Variables
fields = {
'scalar_si': ((1, 1), 'Omega', 2),
'vector_si': ((3, 1), 'Omega', 2),
'scalar_tp': ((1, 1), 'Omega', 1),
'vector_tp': ((3, 1), 'Omega', 1),
}
d1 = Domain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
f = fields[field_name]
field1 = H1NodalVolumeField('f',
nm.float64,
f[0],
d1.regions[f[1]],
approx_order=f[2])
ff = {field1.name: field1}
vv = Variables.from_conf(transform_variables(variables), ff)
u1 = vv['u']
u1.set_from_mesh_vertices(data)
d2 = Domain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = H1NodalVolumeField('f',
nm.float64,
f[0],
d2.regions[f[1]],
approx_order=f[2])
ff2 = {field2.name: field2}
vv2 = Variables.from_conf(transform_variables(variables), ff2)
u2 = vv2['u']
if not force:
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)
else:
coors = u2.field.get_coor()
vals = u1.evaluate_at(coors, close_limit=0.5)
u2.set_data(vals)
return u1, u2
def __init__(self, equations, setup=True,
make_virtual=False, verbose=True):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
if setup:
self.setup(make_virtual=make_virtual, verbose=verbose)
def standalone_setup(self):
from sfepy.fem import create_adof_conns, Variables
conn_info = {'aux' : self.get_conn_info()}
adcs = create_adof_conns(conn_info, None)
variables = Variables(self.get_variables())
variables.set_adof_conns(adcs)
materials = self.get_materials(join=True)
for mat in materials:
mat.time_update(None, [Struct(terms=[self])])
def do_interpolation(m2, m1, data, field_name, force=False):
"""Interpolate data from m1 to m2. """
from sfepy.fem import Domain, H1NodalVolumeField, Variables
fields = {
'scalar_si' : ((1,1), 'Omega', 2),
'vector_si' : ((3,1), 'Omega', 2),
'scalar_tp' : ((1,1), 'Omega', 1),
'vector_tp' : ((3,1), 'Omega', 1),
}
d1 = Domain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
f = fields[field_name]
field1 = H1NodalVolumeField('f', nm.float64, f[0], d1.regions[f[1]],
approx_order=f[2])
ff = {field1.name : field1}
vv = Variables.from_conf(transform_variables(variables), ff)
u1 = vv['u']
u1.set_from_mesh_vertices(data)
d2 = Domain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = H1NodalVolumeField('f', nm.float64, f[0], d2.regions[f[1]],
approx_order=f[2])
ff2 = {field2.name : field2}
vv2 = Variables.from_conf(transform_variables(variables), ff2)
u2 = vv2['u']
if not force:
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)
else:
coors = u2.field.get_coor()
vals = u1.evaluate_at(coors, close_limit=0.5)
u2.set_data(vals)
return u1, u2
def __init__(self, equations, setup=True, caches=None, cache_override=False, make_virtual=False, verbose=True):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.caches = get_default(caches, DataCaches())
self.clear_geometries()
if setup:
self.setup(cache_override=cache_override, make_virtual=make_virtual, verbose=verbose)
def __init__(self, equations):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
self.collect_conn_info()
def __init__(self, equations, setup=True, make_virtual=False, verbose=True):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
if setup:
self.setup(make_virtual=make_virtual, verbose=verbose)
def test_pbc(self):
from sfepy.fem import Variables, Conditions
problem = self.problem
conf = self.conf
ebcs = Conditions.from_conf(conf.ebcs, problem.domain.regions)
epbcs = Conditions.from_conf(conf.epbcs, problem.domain.regions)
variables = Variables.from_conf(conf.variables, problem.fields)
variables.equation_mapping(ebcs, epbcs, None, problem.functions)
state = variables.create_state_vector()
variables.apply_ebc(state)
return variables.has_ebc(state)
def test_pbc( self ):
from sfepy.fem import Variables, Conditions
problem = self.problem
conf = self.conf
ebcs = Conditions.from_conf(conf.ebcs, problem.domain.regions)
epbcs = Conditions.from_conf(conf.epbcs, problem.domain.regions)
variables = Variables.from_conf(conf.variables, problem.fields)
variables.equation_mapping(ebcs, epbcs, None, problem.functions)
state = variables.create_state_vector()
variables.apply_ebc(state)
return variables.has_ebc(state)
def test_invariance_qp(self):
from sfepy import data_dir
from sfepy.fem import (Mesh, Domain, H1NodalVolumeField, Variables,
Integral)
from sfepy.terms import Term
from sfepy.fem.mappings import get_physical_qps
mesh = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')
bbox = mesh.get_bounding_box()
dd = bbox[1, :] - bbox[0, :]
data = nm.sin(4.0 * nm.pi * mesh.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * mesh.coors[:,1:2] / dd[1])
variables = {
'u': ('unknown field', 'scalar_tp', 0),
'v': ('test field', 'scalar_tp', 'u'),
}
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = H1NodalVolumeField('scalar_tp',
nm.float64,
1,
omega,
approx_order=1)
ff = {field.name: field}
vv = Variables.from_conf(transform_variables(variables), ff)
u = vv['u']
u.set_from_mesh_vertices(data)
integral = Integral('i', order=2)
term = Term.new('ev_volume_integrate(u)', integral, omega, u=u)
term.setup()
val1, _ = term.evaluate(mode='qp')
val1 = val1.ravel()
qps = get_physical_qps(omega, integral)
coors = qps.get_merged_values()
val2 = u.evaluate_at(coors).ravel()
self.report('max. difference:', nm.abs(val1 - val2).max())
ok = nm.allclose(val1, val2, rtol=0.0, atol=1e-12)
self.report('invariance in qp: %s' % ok)
return ok
def test_consistency_d_dw( self ):
from sfepy.fem import Function, Variables
ok = True
pb = self.problem
for aux in test_terms:
term_template, (prefix, par_name, d_vars, dw_vars, mat_mode) = aux
print term_template, prefix, par_name, d_vars, dw_vars, mat_mode
term1 = term_template % ((prefix,) + d_vars)
variables = Variables.from_conf(self.conf.variables, pb.fields)
for var_name in d_vars:
var = variables[var_name]
n_dof = var.field.n_nod * var.field.shape[0]
aux = nm.arange( n_dof, dtype = nm.float64 )
var.data_from_data(aux)
pb.materials['m'].function.set_extra_args(term = mat_mode)
if prefix == 'd':
val1 = pb.evaluate(term1, var_dict=variables.as_dict())
else:
val1 = pb.evaluate(term1, call_mode='d_eval',
var_dict=variables.as_dict())
self.report( '%s: %s' % (term1, val1) )
term2 = term_template % (('dw',) + dw_vars[:2])
vec, vv = pb.evaluate(term2, mode='weak',
var_dict=variables.as_dict(),
ret_variables=True)
pvec = vv.get_state_part_view(vec, dw_vars[2])
val2 = nm.dot( variables[par_name](), pvec )
self.report( '%s: %s' % (term2, val2) )
err = nm.abs( val1 - val2 ) / nm.abs( val1 )
_ok = err < 1e-12
self.report( 'relative difference: %e -> %s' % (err, _ok) )
ok = ok and _ok
return ok
def test_consistency_d_dw(self):
from sfepy.fem import Variables
ok = True
pb = self.problem
for aux in test_terms:
term_template, (prefix, par_name, d_vars, dw_vars) = aux
print term_template, prefix, par_name, d_vars, dw_vars
term1 = term_template % ((prefix, ) + d_vars)
variables = Variables.from_conf(self.conf.variables, pb.fields)
for var_name in d_vars:
var = variables[var_name]
n_dof = var.field.n_nod * var.field.shape[0]
aux = nm.arange(n_dof, dtype=nm.float64)
var.set_data(aux)
if prefix == 'd':
val1 = pb.evaluate(term1, var_dict=variables.as_dict())
else:
val1 = pb.evaluate(term1,
call_mode='d_eval',
var_dict=variables.as_dict())
self.report('%s: %s' % (term1, val1))
term2 = term_template % (('dw', ) + dw_vars[:2])
vec, vv = pb.evaluate(term2,
mode='weak',
var_dict=variables.as_dict(),
ret_variables=True)
pvec = vv.get_state_part_view(vec, dw_vars[2])
val2 = nm.dot(variables[par_name](), pvec)
self.report('%s: %s' % (term2, val2))
err = nm.abs(val1 - val2) / nm.abs(val1)
_ok = err < 1e-12
self.report('relative difference: %e -> %s' % (err, _ok))
ok = ok and _ok
return ok
def test_invariance_qp(self):
from sfepy import data_dir
from sfepy.fem import (Mesh, Domain, H1NodalVolumeField,
Variables, Integral)
from sfepy.terms import Term
from sfepy.fem.mappings import get_physical_qps
mesh = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')
bbox = mesh.get_bounding_box()
dd = bbox[1,:] - bbox[0,:]
data = nm.sin(4.0 * nm.pi * mesh.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * mesh.coors[:,1:2] / dd[1])
variables = {
'u' : ('unknown field', 'scalar_tp', 0),
'v' : ('test field', 'scalar_tp', 'u'),
}
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = H1NodalVolumeField('scalar_tp', nm.float64, 1, omega,
approx_order=1)
ff = {field.name : field}
vv = Variables.from_conf(transform_variables(variables), ff)
u = vv['u']
u.set_from_mesh_vertices(data)
integral = Integral('i', order=2)
term = Term.new('ev_volume_integrate(u)', integral, omega, u=u)
term.setup()
val1, _ = term.evaluate(mode='qp')
val1 = val1.ravel()
qps = get_physical_qps(omega, integral)
coors = qps.get_merged_values()
val2 = u.evaluate_at(coors).ravel()
self.report('max. difference:', nm.abs(val1 - val2).max())
ok = nm.allclose(val1, val2, rtol=0.0, atol=1e-12)
self.report('invariance in qp: %s' % ok)
return ok
def test_consistency_d_dw(self):
from sfepy.fem import Variables
ok = True
pb = self.problem
for aux in test_terms:
term_template, (prefix, par_name, d_vars, dw_vars) = aux
print term_template, prefix, par_name, d_vars, dw_vars
term1 = term_template % ((prefix,) + d_vars)
variables = Variables.from_conf(self.conf.variables, pb.fields)
for var_name in d_vars:
var = variables[var_name]
n_dof = var.field.n_nod * var.field.shape[0]
aux = nm.arange(n_dof, dtype=nm.float64)
var.set_data(aux)
if prefix == "d":
val1 = pb.evaluate(term1, var_dict=variables.as_dict())
else:
val1 = pb.evaluate(term1, call_mode="d_eval", var_dict=variables.as_dict())
self.report("%s: %s" % (term1, val1))
term2 = term_template % (("dw",) + dw_vars[:2])
vec, vv = pb.evaluate(term2, mode="weak", var_dict=variables.as_dict(), ret_variables=True)
pvec = vv.get_state_part_view(vec, dw_vars[2])
val2 = nm.dot(variables[par_name](), pvec)
self.report("%s: %s" % (term2, val2))
err = nm.abs(val1 - val2) / nm.abs(val1)
_ok = err < 1e-12
self.report("relative difference: %e -> %s" % (err, _ok))
ok = ok and _ok
return ok
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain):
from sfepy.base.base import basestr
from sfepy.fem import Field, FieldVariable, Material, Variables, Materials
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 5
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh), )
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii,
nm.float64,
shape,
omega,
approx_order=1)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field, shape)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v',
'test',
field,
shape,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field, shape)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii,
'parameter',
field,
shape,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
# Array.
values = {
'%sc%d' % (prefix, ii): nm.ones(shape, dtype=nm.float64)
}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii: 1.0}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
def save_basis_on_mesh(mesh,
options,
output_dir,
lin,
permutations=None,
suffix=''):
if permutations is not None:
mesh = mesh.copy()
for ig, conn in enumerate(mesh.conns):
gel = GeometryElement(mesh.descs[ig])
perms = gel.get_conn_permutations()[permutations]
n_el, n_ep = conn.shape
offsets = nm.arange(n_el) * n_ep
conn[:] = conn.take(perms + offsets[:, None])
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f',
nm.float64,
shape=1,
region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field, 1)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
group = domain.groups[0]
ax = pd.plot_mesh(None, mesh.coors, mesh.conns[0], group.gel.edges)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.aps[0].econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.aps[0].econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.aps[0].econn,
field.aps[0].interp.poly_spaces['v'].nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir,
'dof_%s%s.vtk' % (_format, suffix))
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u',
'f', {'f': field},
None,
Variables([var]),
mode='qp',
verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
ensure_path(name)
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
def create_evaluable(expression, fields, materials, variables, integrals,
regions=None,
ebcs=None, epbcs=None, lcbcs=None, ts=None, functions=None,
auto_init=False, mode='eval', extra_args=None,
verbose=True, kwargs=None):
"""
Create evaluable object (equations and corresponding variables)
from the `expression` string.
Parameters
----------
expression : str
The expression to evaluate.
fields : dict
The dictionary of fields used in `variables`.
materials : Materials instance
The materials used in the expression.
variables : Variables instance
The variables used in the expression.
integrals : Integrals instance
The integrals to be used.
regions : Region instance or list of Region instances
The region(s) to be used. If not given, the regions defined
within the fields domain are used.
ebcs : Conditions instance, optional
The essential (Dirichlet) boundary conditions for 'weak'
mode.
epbcs : Conditions instance, optional
The periodic boundary conditions for 'weak'
mode.
lcbcs : Conditions instance, optional
The linear combination boundary conditions for 'weak'
mode.
ts : TimeStepper instance, optional
The time stepper.
functions : Functions instance, optional
The user functions for boundary conditions, materials
etc.
auto_init : bool
Set values of all variables to all zeros.
mode : one of 'eval', 'el_avg', 'qp', 'weak'
The evaluation mode - 'weak' means the finite element
assembling, 'qp' requests the values in quadrature points,
'el_avg' element averages and 'eval' means integration over
each term region.
extra_args : dict, optional
Extra arguments to be passed to terms in the expression.
verbose : bool
If False, reduce verbosity.
kwargs : dict, optional
The variables (dictionary of (variable name) : (Variable
instance)) to be used in the expression.
Returns
-------
equation : Equation instance
The equation that is ready to be evaluated.
variables : Variables instance
The variables used in the equation.
"""
if kwargs is None:
kwargs = {}
if regions is not None:
if isinstance(regions, Region):
regions = [regions]
regions = OneTypeList(Region, regions)
else:
regions = fields[fields.keys()[0]].domain.regions
# Create temporary variables.
aux_vars = Variables(variables)
if extra_args is None:
extra_args = kwargs
else:
extra_args = copy(extra_args)
extra_args.update(kwargs)
if ts is not None:
extra_args.update({'ts' : ts})
equations = Equations.from_conf({'tmp' : expression},
aux_vars, regions, materials, integrals,
setup=False, user=extra_args,
verbose=verbose)
equations.collect_conn_info()
# The true variables used in the expression.
variables = equations.variables
if auto_init:
for var in variables:
var.init_data(step=0)
if mode == 'weak':
setup_dof_conns(equations.conn_info, verbose=verbose)
equations.time_update(ts, ebcs, epbcs, lcbcs, functions,
verbose=verbose)
else:
setup_extra_data(equations.conn_info)
return equations, variables
class Equations( Container ):
@staticmethod
def from_conf(conf, variables, regions, materials, integrals,
setup=True, user=None,
make_virtual=False, verbose=True):
objs = OneTypeList(Equation)
conf = copy(conf)
ii = 0
for name, desc in conf.iteritems():
if verbose:
output('equation "%s":' % name)
output(desc)
eq = Equation.from_desc(name, desc, variables, regions,
materials, integrals, user=user)
objs.append(eq)
ii += 1
obj = Equations(objs, setup=setup,
make_virtual=make_virtual, verbose=verbose)
return obj
def __init__(self, equations, setup=True,
make_virtual=False, verbose=True):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
if setup:
self.setup(make_virtual=make_virtual, verbose=verbose)
def get_domain(self):
domain = None
for eq in self:
for term in eq.terms:
if term.has_region:
domain = term.region.domain
return domain
def setup(self, make_virtual=False, verbose=True):
self.collect_conn_info()
# This uses the conn_info created above.
self.dof_conns = {}
setup_dof_conns(self.conn_info, dof_conns=self.dof_conns,
make_virtual=make_virtual, verbose=verbose)
def collect_materials(self):
"""
Collect materials present in the terms of all equations.
"""
materials = []
for eq in self:
materials.extend(eq.collect_materials())
# Make the list items unique.
materials = list(set(materials))
return materials
def reset_materials(self):
"""
Clear material data so that next materials.time_update() is
performed even for stationary materials.
"""
self.materials.reset()
def collect_variables(self):
"""
Collect variables present in the terms of all equations.
"""
variables = []
for eq in self:
variables.extend(eq.collect_variables())
# Make the list items unique.
variables = list(set(variables))
return variables
def get_variable(self, name):
var = self.variables.get(name,
msg_if_none='unknown variable! (%s)' % name)
return var
def collect_conn_info(self):
"""
Collect connectivity information as defined by the equations.
"""
self.conn_info = {}
for eq in self:
eq.collect_conn_info(self.conn_info)
## print_structs(self.conn_info)
## pause()
return self.conn_info
def get_variable_names( self ):
"""Return the list of names of all variables used in equations."""
vns = set()
for eq in self:
for term in eq.terms:
vns.update( term.get_variable_names() )
return list( vns )
def invalidate_term_caches(self):
"""
Invalidate evaluate caches of variables present in equations.
"""
for var in self.variables:
var.invalidate_evaluate_cache()
def print_terms(self):
"""
Print names of equations and their terms.
"""
output('equations:')
for eq in self:
output(' %s:' % eq.name)
for term in eq.terms:
output(' %+.2e * %s.%d.%s(%s)'
% (term.sign, term.name, term.integral.order,
term.region.name, term.arg_str))
def time_update(self, ts, ebcs=None, epbcs=None, lcbcs=None,
functions=None, problem=None, verbose=True):
"""
Update the equations for current time step.
The update involves creating the mapping of active DOFs from/to
all DOFs for all state variables, the setup of linear
combination boundary conditions operators and the setup of
active DOF connectivities.
Parameters
----------
ts : TimeStepper instance
The time stepper.
ebcs : Conditions instance, optional
The essential (Dirichlet) boundary conditions.
epbcs : Conditions instance, optional
The periodic boundary conditions.
lcbcs : Conditions instance, optional
The linear combination boundary conditions.
functions : Functions instance, optional
The user functions for boundary conditions, materials, etc.
problem : ProblemDefinition instance, optional
The problem that can be passed to user functions as a context.
verbose : bool
If False, reduce verbosity.
Returns
-------
graph_changed : bool
The flag set to True if the current time step set of active
boundary conditions differs from the set of the previous
time step.
"""
self.variables.time_update(ts, functions, verbose=verbose)
active_bcs = self.variables.equation_mapping(ebcs, epbcs, ts, functions,
problem=problem)
graph_changed = active_bcs != self.active_bcs
self.active_bcs = active_bcs
self.variables.setup_lcbc_operators(lcbcs, ts, functions)
self.variables.setup_adof_conns()
for eq in self:
for term in eq.terms:
term.time_update(ts)
return graph_changed
def time_update_materials(self, ts, mode='normal', problem=None,
verbose=True):
"""
Update data materials for current time and possibly also state.
Parameters
----------
ts : TimeStepper instance
The time stepper.
mode : 'normal', 'update' or 'force'
The update mode, see
:func:`sfepy.fem.materials.Material.time_update()`.
problem : ProblemDefinition instance, optional
The problem that can be passed to user functions as a context.
verbose : bool
If False, reduce verbosity.
"""
self.materials.time_update(ts, self, mode=mode, problem=problem,
verbose=verbose)
def setup_initial_conditions(self, ics, functions):
self.variables.setup_initial_conditions(ics, functions)
def get_graph_conns(self, any_dof_conn=False, rdcs=None, cdcs=None):
"""
Get DOF connectivities needed for creating tangent matrix graph.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
Returns
-------
rdcs, cdcs : arrays
The row and column DOF connectivities defining the matrix
graph blocks.
"""
if rdcs is None:
rdcs = []
cdcs = []
elif cdcs is None:
cdcs = copy(rdcs)
else:
assert_(len(rdcs) == len(cdcs))
if rdcs is cdcs: # Make sure the lists are not the same object.
rdcs = copy(rdcs)
adcs = self.variables.adof_conns
# Only volume dof connectivities are used, with the exception of trace
# surface dof connectivities.
shared = set()
for key, ii, info in iter_dict_of_lists(self.conn_info,
return_keys=True):
rvar, cvar = info.virtual, info.state
if (rvar is None) or (cvar is None):
continue
is_surface = rvar.is_surface or cvar.is_surface
dct = info.dc_type.type
if not (dct in ('volume', 'scalar') or is_surface
or info.is_trace or any_dof_conn):
continue
rreg_name = info.get_region_name(can_trace=False)
creg_name = info.get_region_name()
for rig, cig in info.iter_igs():
rname = rvar.get_primary_name()
rkey = (rname, rreg_name, dct, rig, False)
ckey = (cvar.name, creg_name, dct, cig, info.is_trace)
dc_key = (rkey, ckey)
## print dc_key
if not dc_key in shared:
try:
rdcs.append(adcs[rkey])
cdcs.append(adcs[ckey])
except:
debug()
shared.add(dc_key)
return rdcs, cdcs
def create_matrix_graph(self, any_dof_conn=False, rdcs=None, cdcs=None,
shape=None):
"""
Create tangent matrix graph, i.e. preallocate and initialize the
sparse storage needed for the tangent matrix. Order of DOF
connectivities is not important.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
shape : tuple, optional
The required shape, if it is different from the shape
determined by the equations variables. This may be needed if
additional row and column DOF connectivities are passed in.
Returns
-------
matrix : csr_matrix
The matrix graph in the form of a CSR matrix with
preallocated structure and zero data.
"""
if not self.variables.has_virtuals():
output('no matrix (no test variables)!')
return None
shape = get_default(shape, self.variables.get_matrix_shape())
output( 'matrix shape:', shape )
if nm.prod( shape ) == 0:
output( 'no matrix (zero size)!' )
return None
rdcs, cdcs = self.get_graph_conns(any_dof_conn=any_dof_conn,
rdcs=rdcs, cdcs=cdcs)
if not len(rdcs):
output('no matrix (empty dof connectivities)!')
return None
output( 'assembling matrix graph...' )
tt = time.clock()
nnz, prow, icol = create_mesh_graph(shape[0], shape[1],
len(rdcs), rdcs, cdcs)
output( '...done in %.2f s' % (time.clock() - tt) )
output( 'matrix structural nonzeros: %d (%.2e%% fill)' \
% (nnz, float( nnz ) / nm.prod( shape ) ) )
## print ret, prow, icol, nnz
data = nm.zeros( (nnz,), dtype = self.variables.dtype )
matrix = sp.csr_matrix( (data, icol, prow), shape )
## matrix.save( 'matrix', format = '%d %d %e\n' )
## pause()
return matrix
##
# c: 02.04.2008, r: 02.04.2008
def init_time( self, ts ):
pass
##
# 08.06.2007, c
def advance( self, ts ):
for eq in self:
for term in eq.terms:
term.advance(ts)
self.variables.advance(ts)
##
# Interface to self.variables.
def create_state_vector(self):
return self.variables.create_state_vector()
def create_stripped_state_vector(self):
return self.variables.create_stripped_state_vector()
def strip_state_vector(self, vec, follow_epbc=False):
"""
Strip a full vector by removing EBC dofs.
Notes
-----
If 'follow_epbc' is True, values of EPBC master dofs are not simply
thrown away, but added to the corresponding slave dofs, just like when
assembling. For vectors with state (unknown) variables it should be set
to False, for assembled vectors it should be set to True.
"""
return self.variables.strip_state_vector(vec, follow_epbc=follow_epbc)
def make_full_vec(self, svec, force_value=None):
"""
Make a full DOF vector satisfying E(P)BCs from a reduced DOF
vector.
"""
return self.variables.make_full_vec(svec, force_value)
def set_variables_from_state(self, vec, step=0):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : array
The state vector.
step : int
The time history step, 0 (default) = current.
"""
self.variables.set_data(vec, step=step)
def get_state_parts(self, vec=None):
"""
Return parts of a state vector corresponding to individual state
variables.
Parameters
----------
vec : array, optional
The state vector. If not given, then the data stored in the
variables are returned instead.
Returns
-------
out : dict
The dictionary of the state parts.
"""
return self.variables.get_state_parts(vec)
def set_data(self, data, step=0, ignore_unknown=False):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : array
The dictionary of {variable_name : data vector}.
step : int, optional
The time history step, 0 (default) = current.
ignore_unknown : bool, optional
Ignore unknown variable names if `data` is a dict.
"""
self.variables.set_data(data, step=step,
ignore_unknown=ignore_unknown)
def apply_ebc(self, vec, force_values=None):
"""
Apply essential (Dirichlet) boundary conditions to a state vector.
"""
self.variables.apply_ebc(vec, force_values=force_values)
def apply_ic(self, vec, force_values=None):
"""
Apply initial conditions to a state vector.
"""
self.variables.apply_ic(vec, force_values=force_values)
def state_to_output(self, vec, fill_value=None, var_info=None,
extend=True):
return self.variables.state_to_output(vec,
fill_value=fill_value,
var_info=var_info,
extend=extend)
def get_lcbc_operator(self):
return self.variables.get_lcbc_operator()
def evaluate(self, mode='eval', dw_mode='vector', term_mode=None,
asm_obj=None):
"""
Parameters
----------
mode : one of 'eval', 'el_avg', 'qp', 'weak'
The evaluation mode.
"""
if mode == 'weak':
out = asm_obj
else:
out = {}
for eq in self:
eout = eq.evaluate(mode=mode, dw_mode=dw_mode, term_mode=term_mode,
asm_obj=asm_obj)
if mode != 'weak':
out[eq.name] = eout
if (len(self) == 1) and (mode != 'weak'):
out = out.popitem()[1]
return out
def eval_residuals(self, state, by_blocks=False, names=None):
"""
Evaluate (assemble) residual vectors.
Parameters
----------
state : array
The vector of DOF values. Note that it is needed only in
nonlinear terms.
by_blocks : bool
If True, return the individual blocks composing the whole
residual vector. Each equation should then correspond to one
required block and should be named as `'block_name,
test_variable_name, unknown_variable_name'`.
names : list of str, optional
Optionally, select only blocks with the given `names`, if
`by_blocks` is True.
Returns
-------
out : array or dict of array
The assembled residual vector. If `by_blocks` is True, a
dictionary is returned instead, with keys given by
`block_name` part of the individual equation names.
"""
self.set_variables_from_state(state)
if by_blocks:
names = get_default(names, self.names)
out = {}
get_indx = self.variables.get_indx
for name in names:
eq = self[name]
key, rname, cname = [aux.strip()
for aux in name.split(',')]
ir = get_indx(rname, stripped=True, allow_dual=True)
residual = self.create_stripped_state_vector()
eq.evaluate(mode='weak', dw_mode='vector', asm_obj=residual)
out[key] = residual[ir]
else:
out = self.create_stripped_state_vector()
self.evaluate(mode='weak', dw_mode='vector', asm_obj=out)
return out
def eval_tangent_matrices(self, state, tangent_matrix,
by_blocks=False, names=None):
"""
Evaluate (assemble) tangent matrices.
Parameters
----------
state : array
The vector of DOF values. Note that it is needed only in
nonlinear terms.
tangent_matrix : csr_matrix
The preallocated CSR matrix with zero data.
by_blocks : bool
If True, return the individual blocks composing the whole
matrix. Each equation should then correspond to one
required block and should be named as `'block_name,
test_variable_name, unknown_variable_name'`.
names : list of str, optional
Optionally, select only blocks with the given `names`, if
`by_blocks` is True.
Returns
-------
out : csr_matrix or dict of csr_matrix
The assembled matrix. If `by_blocks` is True, a dictionary
is returned instead, with keys given by `block_name` part
of the individual equation names.
"""
self.set_variables_from_state(state)
if by_blocks:
names = get_default(names, self.names)
out = {}
get_indx = self.variables.get_indx
for name in names:
eq = self[name]
key, rname, cname = [aux.strip()
for aux in eq.name.split(',')]
ir = get_indx(rname, stripped=True, allow_dual=True)
ic = get_indx(cname, stripped=True, allow_dual=True)
tangent_matrix.data[:] = 0.0
eq.evaluate(mode='weak', dw_mode='matrix',
asm_obj=tangent_matrix)
out[key] = tangent_matrix[ir, ic]
else:
tangent_matrix.data[:] = 0.0
self.evaluate(mode='weak', dw_mode='matrix', asm_obj=tangent_matrix)
out = tangent_matrix
return out
class Equations(Container):
@staticmethod
def from_conf(
conf,
variables,
regions,
materials,
integrals,
setup=True,
caches=None,
user=None,
cache_override=False,
make_virtual=False,
verbose=True,
):
objs = OneTypeList(Equation)
conf = copy(conf)
if caches is None:
caches = DataCaches()
ii = 0
for name, desc in conf.iteritems():
if verbose:
output('equation "%s":' % name)
output(desc)
eq = Equation.from_desc(name, desc, variables, regions, materials, integrals, caches=caches, user=user)
objs.append(eq)
ii += 1
obj = Equations(
objs, setup=setup, caches=caches, cache_override=cache_override, make_virtual=make_virtual, verbose=verbose
)
return obj
def __init__(self, equations, setup=True, caches=None, cache_override=False, make_virtual=False, verbose=True):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.caches = get_default(caches, DataCaches())
self.clear_geometries()
if setup:
self.setup(cache_override=cache_override, make_virtual=make_virtual, verbose=verbose)
def clear_geometries(self):
self.geometries = {}
def setup(self, cache_override=False, make_virtual=False, verbose=True):
self.collect_conn_info()
# This uses the conn_info created above.
self.dof_conns = {}
setup_dof_conns(self.conn_info, dof_conns=self.dof_conns, make_virtual=make_virtual, verbose=verbose)
self.assign_geometries()
self.set_cache_mode(cache_override)
def collect_materials(self):
"""
Collect materials present in the terms of all equations.
"""
materials = []
for eq in self:
materials.extend(eq.collect_materials())
# Make the list items unique.
materials = list(set(materials))
return materials
def collect_variables(self):
"""
Collect variables present in the terms of all equations.
"""
variables = []
for eq in self:
variables.extend(eq.collect_variables())
# Make the list items unique.
variables = list(set(variables))
return variables
def get_variable(self, name):
var = self.variables.get(name, msg_if_none="unknown variable! (%s)" % name)
return var
def collect_conn_info(self):
"""
Collect connectivity information as defined by the equations.
"""
self.conn_info = {}
for eq in self:
eq.collect_conn_info(self.conn_info)
## print_structs(self.conn_info)
## pause()
return self.conn_info
def assign_geometries(self):
for eq in self:
eq.assign_geometries(self.geometries)
def get_variable_names(self):
"""Return the list of names of all variables used in equations."""
vns = set()
for eq in self:
for term in eq.terms:
vns.update(term.get_variable_names())
return list(vns)
##
# 27.02.2007, c
def invalidate_term_caches(self):
for cache in self.caches.itervalues():
cache.clear()
##
# c: 07.05.2008, r: 07.05.2008
def reset_term_caches(self):
for cache in self.caches.itervalues():
cache.reset()
##
# 02.03.2007, c
def set_cache_mode(self, cache_override):
for cache in self.caches.itervalues():
cache.set_mode(cache_override)
def time_update(self, ts, ebcs=None, epbcs=None, lcbcs=None, functions=None):
self.variables.time_update(ts, functions)
self.variables.equation_mapping(ebcs, epbcs, ts, functions)
self.variables.setup_lcbc_operators(lcbcs)
self.variables.setup_adof_conns()
for eq in self:
for term in eq.terms:
term.time_update(ts)
def setup_initial_conditions(self, ics, functions):
self.variables.setup_initial_conditions(ics, functions)
def get_graph_conns(self, any_dof_conn=False, rdcs=None, cdcs=None):
"""
Get DOF connectivities needed for creating tangent matrix graph.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
Returns
-------
rdcs, cdcs : arrays
The row and column DOF connectivities defining the matrix
graph blocks.
"""
if rdcs is None:
rdcs = []
cdcs = []
elif cdcs is None:
cdcs = copy(rdcs)
else:
assert_(len(rdcs) == len(cdcs))
if rdcs is cdcs: # Make sure the lists are not the same object.
rdcs = copy(rdcs)
adcs = self.variables.adof_conns
# Only volume dof connectivities are used, with the exception of trace
# surface dof connectivities.
shared = set()
for key, ii, info in iter_dict_of_lists(self.conn_info, return_keys=True):
rvar, cvar = info.virtual, info.state
if (rvar is None) or (cvar is None):
continue
is_surface = rvar.is_surface or cvar.is_surface
dct = info.dc_type.type
if not (dct in ("volume", "scalar") or is_surface or info.is_trace or any_dof_conn):
continue
rreg_name = info.get_region_name(can_trace=False)
creg_name = info.get_region_name()
for rig, cig in info.iter_igs():
rname = rvar.get_primary_name()
rkey = (rname, rreg_name, dct, rig)
ckey = (cvar.name, creg_name, dct, cig)
dc_key = (rkey, ckey)
## print dc_key
if not dc_key in shared:
try:
rdcs.append(adcs[rkey])
cdcs.append(adcs[ckey])
except:
debug()
shared.add(dc_key)
## print shared
for ii in range(len(rdcs)):
if (rdcs[ii].ndim == 1) and (cdcs[ii].ndim == 2):
rdcs[ii] = _fix_scalar_dc(rdcs[ii], cdcs[ii])
elif (cdcs[ii].ndim == 1) and (rdcs[ii].ndim == 2):
cdcs[ii] = _fix_scalar_dc(cdcs[ii], rdcs[ii])
elif (cdcs[ii].ndim == 1) and (rdcs[ii].ndim == 1):
rdcs[ii] = nm.array(rdcs[ii], ndmin=2)
cdcs[ii] = nm.array(cdcs[ii], ndmin=2)
return rdcs, cdcs
def create_matrix_graph(self, any_dof_conn=False, rdcs=None, cdcs=None, shape=None):
"""
Create tangent matrix graph, i.e. preallocate and initialize the
sparse storage needed for the tangent matrix. Order of DOF
connectivities is not important.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
shape : tuple, optional
The required shape, if it is different from the shape
determined by the equations variables. This may be needed if
additional row and column DOF connectivities are passed in.
Returns
-------
matrix : csr_matrix
The matrix graph in the form of a CSR matrix with
preallocated structure and zero data.
"""
if not self.variables.has_virtuals():
output("no matrix (no test variables)!")
return None
shape = get_default(shape, self.variables.get_matrix_shape())
output("matrix shape:", shape)
if nm.prod(shape) == 0:
output("no matrix (zero size)!")
return None
rdcs, cdcs = self.get_graph_conns(any_dof_conn=any_dof_conn, rdcs=rdcs, cdcs=cdcs)
if not len(rdcs):
output("no matrix (empty dof connectivities)!")
return None
output("assembling matrix graph...")
tt = time.clock()
ret, prow, icol = raw_graph(int(shape[0]), int(shape[1]), len(rdcs), rdcs, cdcs)
output("...done in %.2f s" % (time.clock() - tt))
nnz = prow[-1]
output("matrix structural nonzeros: %d (%.2e%% fill)" % (nnz, float(nnz) / nm.prod(shape)))
## print ret, prow, icol, nnz
data = nm.zeros((nnz,), dtype=self.variables.dtype)
matrix = sp.csr_matrix((data, icol, prow), shape)
## matrix.save( 'matrix', format = '%d %d %e\n' )
## pause()
return matrix
##
# c: 02.04.2008, r: 02.04.2008
def init_time(self, ts):
for cache in self.caches.itervalues():
cache.init_time(ts)
##
# 08.06.2007, c
def advance(self, ts):
for cache in self.caches.itervalues():
cache.advance(ts.step + 1)
for eq in self:
for term in eq.terms:
term.advance(ts)
self.variables.advance(ts)
##
# Interface to self.variables.
def create_state_vector(self):
return self.variables.create_state_vector()
def create_stripped_state_vector(self):
return self.variables.create_stripped_state_vector()
def strip_state_vector(self, vec, follow_epbc=True):
"""
Strip a full vector by removing EBC dofs. If 'follow_epbc' is True,
values of EPBC master dofs are not simply thrown away, but added to the
corresponding slave dofs, just like when assembling.
"""
return self.variables.strip_state_vector(vec, follow_epbc=follow_epbc)
def make_full_vec(self, svec, var_name=None, force_value=None):
"""
Make a full vector satisfying E(P)BC
from a stripped vector. For a selected variable if var_name is set.
"""
return self.variables.make_full_vec(svec, var_name=var_name, force_value=force_value)
def set_variables_from_state(self, vec, step=0):
"""
Set data (vectors of DOF values) of variables.
Paramters
---------
data : array
The state vector.
step : int
The time history step, 0 (default) = current.
"""
self.variables.set_data(vec, step=step)
def get_state_parts(self, vec=None):
"""
Return parts of a state vector corresponding to individual state
variables.
Parameters
----------
vec : array, optional
The state vector. If not given, then the data stored in the
variables are returned instead.
Returns
-------
out : dict
The dictionary of the state parts.
"""
return self.variables.get_state_parts(vec)
def set_data(self, data, step=0, ignore_unknown=False):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : array
The dictionary of {variable_name : data vector}.
step : int, optional
The time history step, 0 (default) = current.
ignore_unknown : bool, optional
Ignore unknown variable names if `data` is a dict.
"""
self.variables.set_data(data, step=step, ignore_unknown=ignore_unknown)
def apply_ebc(self, vec, force_values=None):
"""
Apply essential (Dirichlet) boundary conditions to a state vector.
"""
self.variables.apply_ebc(vec, force_values=force_values)
def apply_ic(self, vec, force_values=None):
"""
Apply initial conditions to a state vector.
"""
self.variables.apply_ic(vec, force_values=force_values)
def state_to_output(self, vec, fill_value=None, var_info=None, extend=True):
return self.variables.state_to_output(vec, fill_value=fill_value, var_info=var_info, extend=extend)
def get_lcbc_operator(self):
return self.variables.get_lcbc_operator()
def evaluate(self, mode="eval", dw_mode="vector", term_mode=None, asm_obj=None):
"""
Parameters
----------
mode : one of 'eval', 'el_avg', 'qp', 'weak'
The evaluation mode.
"""
if mode == "weak":
out = asm_obj
else:
out = {}
for eq in self:
eout = eq.evaluate(mode=mode, dw_mode=dw_mode, term_mode=term_mode, asm_obj=asm_obj)
if mode != "weak":
out[eq.name] = eout
if (len(self) == 1) and (mode != "weak"):
out = out.popitem()[1]
return out
def eval_residuals(self, state):
self.invalidate_term_caches()
self.set_variables_from_state(state)
residual = self.create_stripped_state_vector()
self.evaluate(mode="weak", dw_mode="vector", asm_obj=residual)
return residual
def eval_tangent_matrices(self, state, tangent_matrix, by_blocks=False):
"""
Evaluate (assemble) tangent matrices.
Parameters
----------
state : array
The vector of DOF values. Note that it is needed only in
nonlinear terms.
tangent_matrix : csr_matrix
The preallocated CSR matrix with zero data.
by_blocks : bool
If True, return the individual blocks composing the whole
matrix. Each equation should then correspond to one
required block and should be named as `'block_name,
test_variable_name, unknown_variable_name'`.
Returns
-------
out : csr_matrix or dict of csr_matrix
The assembled matrix. If `by_blocks` is True, a dictionary
is returned instead, with keys given by `block_name` part
of the individual equation names.
"""
self.set_variables_from_state(state)
self.evaluate(mode="weak", dw_mode="matrix", asm_obj=tangent_matrix)
if by_blocks:
out = {}
get_indx = self.variables.get_indx
for eq in self:
key, rname, cname = [aux.strip() for aux in eq.name.split(",")]
ir = get_indx(rname, stripped=True, allow_dual=True)
ic = get_indx(cname, stripped=True, allow_dual=True)
out[key] = tangent_matrix[ir, ic]
else:
out = tangent_matrix
return out
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-b',
'--basis',
metavar='name',
action='store',
dest='basis',
default='lagrange',
help=help['basis'])
parser.add_option('-d',
'--derivative',
metavar='d',
type=int,
action='store',
dest='derivative',
default=0,
help=help['derivative'])
parser.add_option('-n',
'--max-order',
metavar='order',
type=int,
action='store',
dest='max_order',
default=2,
help=help['max_order'])
parser.add_option('-g',
'--geometry',
metavar='name',
action='store',
dest='geometry',
default='2_4',
help=help['geometry'])
parser.add_option('-m',
'--mesh',
metavar='mesh',
action='store',
dest='mesh',
default=None,
help=help['mesh'])
parser.add_option('',
'--permutations',
metavar='permutations',
action='store',
dest='permutations',
default=None,
help=help['permutations'])
parser.add_option('',
'--dofs',
metavar='dofs',
action='store',
dest='dofs',
default=None,
help=help['dofs'])
parser.add_option('-l',
'--lin-options',
metavar='options',
action='store',
dest='lin_options',
default='min_level=2,max_level=5,eps=1e-3',
help=help['lin_options'])
parser.add_option('',
'--plot-dofs',
action='store_true',
dest='plot_dofs',
default=False,
help=help['plot_dofs'])
options, args = parser.parse_args()
if len(args) == 1:
output_dir = args[0]
else:
parser.print_help(),
return
output('polynomial space:', options.basis)
output('max. order:', options.max_order)
lin = Struct(kind='adaptive', min_level=2, max_level=5, eps=1e-3)
for opt in options.lin_options.split(','):
key, val = opt.split('=')
setattr(lin, key, eval(val))
if options.mesh is None:
dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
output('reference element geometry:')
output(' dimension: %d, vertices: %d' % (dim, n_ep))
gel = GeometryElement(options.geometry)
gps = PolySpace.any_from_args(None, gel, 1, base=options.basis)
ps = PolySpace.any_from_args(None,
gel,
options.max_order,
base=options.basis)
n_digit, _format = get_print_info(ps.n_nod, fill='0')
name_template = os.path.join(output_dir, 'bf_%s.vtk' % _format)
for ip in get_dofs(options.dofs, ps.n_nod):
output('shape function %d...' % ip)
def eval_dofs(iels, rx):
if options.derivative == 0:
bf = ps.eval_base(rx).squeeze()
rvals = bf[None, :, ip:ip + 1]
else:
bfg = ps.eval_base(rx, diff=True)
rvals = bfg[None, ..., ip]
return rvals
def eval_coors(iels, rx):
bf = gps.eval_base(rx).squeeze()
coors = nm.dot(bf, gel.coors)[None, ...]
return coors
(level, coors, conn, vdofs,
mat_ids) = create_output(eval_dofs,
eval_coors,
1,
ps,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
out = {
'bf':
Struct(name='output_data',
mode='vertex',
data=vdofs,
var_name='bf',
dofs=None)
}
mesh = Mesh.from_data('bf_mesh', coors, None, [conn], [mat_ids],
[options.geometry])
name = name_template % ip
mesh.write(name, out=out)
output('...done (%s)' % name)
else:
mesh = Mesh.from_file(options.mesh)
output('mesh geometry:')
output(' dimension: %d, vertices: %d, elements: %d' %
(mesh.dim, mesh.n_nod, mesh.n_el))
domain = Domain('domain', mesh)
if options.permutations:
permutations = [int(ii) for ii in options.permutations.split(',')]
output('using connectivity permutations:', permutations)
for group in domain.iter_groups():
perms = group.gel.get_conn_permutations()[permutations]
offsets = nm.arange(group.shape.n_el) * group.shape.n_ep
group.conn[:] = group.conn.take(perms + offsets[:, None])
domain.setup_facets()
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f',
nm.float64,
shape=1,
region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field, 1)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
group = domain.groups[0]
ax = pd.plot_mesh(None, mesh.coors, mesh.conns[0], group.gel.edges)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.aps[0].econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.aps[0].econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.aps[0].econn,
field.aps[0].interp.poly_spaces['v'].nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir, 'dof_%s.vtk' % _format)
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u',
'f', {'f': field},
None,
Variables([var]),
mode='qp',
verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)