"""
Classes of equations composed of terms.
"""
from copy import copy
import numpy as nm
import scipy.sparse as sp
from sfepy.base.base import output, assert_, get_default, iter_dict_of_lists
from sfepy.base.base import OneTypeList, Container, Struct
from sfepy.base.timing import Timer
from sfepy.discrete import Materials, Variables, create_adof_conns
from sfepy.discrete.common.extmods.cmesh import create_mesh_graph
from sfepy.terms import Terms, Term
from sfepy.terms.terms_multilinear import ETermBase
[docs]def parse_definition(equation_def):
"""
Parse equation definition string to create term description list.
"""
from .parse_equations import create_bnf
term_descs = []
bnf = create_bnf(term_descs)
try:
bnf.parseString(equation_def)
except:
raise ValueError('cannot parse equation! (%s)' % equation_def)
return term_descs
[docs]def get_expression_arg_names(expression, strip_dots=True):
"""
Parse expression and return set of all argument names. For arguments
with attribute-like syntax (e.g. materials), if `strip_dots` is
True, only base argument names are returned.
"""
args = ','.join(aux.args for aux in parse_definition(expression))
args = [arg.strip() for arg in args.split(',')]
if strip_dots:
for ii, arg in enumerate(args[:]):
aux = arg.split('.')
if len(aux) == 2:
args[ii] = aux[0]
return set(args)
[docs]class Equations(Container):
[docs] @staticmethod
def from_conf(conf, variables, regions, materials, integrals,
user=None, eterm_options=None, allow_derivatives=False,
verbose=True):
objs = OneTypeList(Equation)
conf = copy(conf)
ii = 0
for name, desc in conf.items():
if verbose:
output('equation "%s":' % name)
output(desc)
eq = Equation.from_desc(name, desc, variables, regions,
materials, integrals, user=user,
eterm_options=eterm_options,
allow_derivatives=allow_derivatives)
objs.append(eq)
ii += 1
obj = Equations(objs)
return obj
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()
[docs] def add_equation(self, equation):
"""
Add a new equation.
Parameters
----------
equation : Equation instance
The new equation.
"""
self.append(equation)
self.variables.extend(
set(equation.collect_variables() ) - set(self.variables)
)
self.materials.extend(
set(equation.collect_materials() ) - set(self.materials)
)
equation.collect_conn_info(self.conn_info)
if not self.domain:
self.domain = self.get_domain()
[docs] def create_subequations(self, var_names, known_var_names=None):
"""
Create sub-equations containing only terms with the given virtual
variables.
Parameters
----------
var_names : list
The list of names of virtual variables.
known_var_names : list
The list of names of (already) known state variables.
Returns
-------
subequations : Equations instance
The sub-equations.
"""
from sfepy.discrete import FieldVariable
known_var_names = get_default(known_var_names, [])
objs = []
for iv, var_name in enumerate(var_names):
terms = [term.copy(name=term.name)
for eq in self for term in eq.terms
if term.get_virtual_name() == var_name]
# Make parameter variables from known state variables in terms
# arguments.
for known_name in known_var_names:
for term in terms:
if known_name in term.arg_names:
ii = term.arg_names.index(known_name)
state = self.variables[known_name]
par = FieldVariable(known_name, 'parameter',
state.field,
primary_var_name='(set-to-None)')
term.args[ii] = par
term._kwargs[known_name] = par
par.set_data(state())
new_terms = Terms(terms)
objs.append(Equation('eq_%d' % iv, new_terms))
subequations = Equations(objs)
return subequations
[docs] 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
[docs] 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
[docs] def reset_materials(self):
"""
Clear material data so that next materials.time_update() is
performed even for stationary materials.
"""
self.materials.reset()
[docs] 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
[docs] def get_variable(self, name):
var = self.variables.get(name,
msg_if_none='unknown variable! (%s)' % name)
return var
[docs] 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)
return self.conn_info
[docs] 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)
[docs] def get_variable_dependencies(self):
"""
For each virtual variable get names of state/parameter variables that
are present in terms with that virtual variable.
The virtual variables define the actual equations and their
dependencies define the variables needed to evaluate the equations.
Returns
-------
deps : dict
The dependencies as a dictionary with virtual variable names as
keys and sets of state/parameter variables as values.
"""
deps = {}
for eq in self:
for term in eq.terms:
dep_list = deps.setdefault(term.get_virtual_name(), set())
dep_list.update(term.get_state_names())
return deps
[docs] def invalidate_term_caches(self):
"""
Invalidate evaluate caches of variables present in equations.
"""
for var in self.variables:
var.invalidate_evaluate_cache()
[docs] 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(' %s' % term.get_str())
[docs] def time_update(self, ts, ebcs=None, epbcs=None, lcbcs=None,
functions=None, problem=None, active_only=True,
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 : Problem instance, optional
The problem that can be passed to user functions as a context.
active_only : bool
If True, the active DOF connectivities and matrix graph have
reduced size and are created with the reduced (active DOFs only)
numbering.
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,
active_only=active_only)
graph_changed = active_bcs != self.active_bcs
self.active_bcs = active_bcs
if graph_changed or not self.variables.adof_conns:
adcs = create_adof_conns(self.conn_info, self.variables.adi.indx,
active_only=active_only)
self.variables.set_adof_conns(adcs)
self.variables.setup_lcbc_operators(lcbcs, ts, functions)
for eq in self:
for term in eq.terms:
term.time_update(ts)
return graph_changed
[docs] 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.discrete.materials.Material.time_update()`.
problem : Problem 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)
[docs] def setup_initial_conditions(self, ics, functions=None):
self.variables.setup_initial_conditions(ics, functions)
[docs] def get_graph_conns(self, any_dof_conn=False, rdcs=None, cdcs=None,
active_only=True):
"""
Get DOF connectivities needed for creating tangent matrix graph.
Parameters
----------
any_dof_conn : bool
By default, only cell DOF connectivities are used, with
the exception of trace facet 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.
active_only : bool
If True, the active DOF connectivities have reduced size and are
created with the reduced (active DOFs only) numbering.
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 cell dof connectivities are used, with the exception of trace
# facet 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
rreg_name = info.get_region_name(can_trace=False)
creg_name = info.get_region_name()
mreg_name = None if creg_name == rreg_name else rreg_name
rname = rvar.get_primary_name()
cname = cvar.get_primary_name()
rkey = (rname, rreg_name, info.dof_conn_types[rname], None)
ckey = (cvar.name, creg_name, info.dof_conn_types[cname],
mreg_name)
dc_key = (rkey, ckey)
if dc_key not in shared:
rdc = adcs[rkey]
cdc = adcs[ckey]
if not active_only:
ii = nm.where(rdc < 0)
rdc = rdc.copy()
rdc[ii] = -1 - rdc[ii]
ii = nm.where(cdc < 0)
cdc = cdc.copy()
cdc[ii] = -1 - cdc[ii]
rdcs.append(rdc)
cdcs.append(cdc)
shared.add(dc_key)
return rdcs, cdcs
[docs] def create_matrix_graph(self, any_dof_conn=False, rdcs=None, cdcs=None,
shape=None, active_only=True, verbose=True):
"""
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 cell region DOF connectivities are used, with
the exception of trace facet DOF connectivities. If True,
any DOF connectivities are used.
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.
active_only : bool
If True, the matrix graph has reduced size and is created with the
reduced (active DOFs only) numbering.
verbose : bool
If False, reduce verbosity.
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, verbose=verbose)
size = nm.prod(shape, dtype=nm.int64)
if size == 0:
output('no matrix (zero size)!')
return None
rdcs, cdcs = self.get_graph_conns(any_dof_conn=any_dof_conn,
rdcs=rdcs, cdcs=cdcs,
active_only=active_only)
if not len(rdcs):
output('no matrix (empty dof connectivities)!')
return None
output('assembling matrix graph...', verbose=verbose)
timer = Timer(start=True)
nnz, prow, icol = create_mesh_graph(shape[0], shape[1],
len(rdcs), rdcs, cdcs)
output('...done in %.2f s' % timer.stop(), verbose=verbose)
output('matrix structural nonzeros: %d (%.2e%% fill)' \
% (nnz, 100.0 * float(nnz) / size), verbose=verbose)
data = nm.zeros((nnz,), dtype=self.variables.dtype)
matrix = sp.csr_matrix((data, icol, prow), shape)
return matrix
[docs] def init_time(self, ts):
pass
[docs] def advance(self, ts):
for eq in self:
for term in eq.terms:
term.advance(ts)
self.variables.advance(ts)
##
# Interface to self.variables.
[docs] def create_vec(self):
return self.variables.create_vec()
[docs] def create_reduced_vec(self):
return self.variables.create_reduced_vec()
[docs] def reduce_vec(self, vec, follow_epbc=False):
"""
Get the reduced DOF vector, with EBC and PBC DOFs removed.
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.reduce_vec(vec, follow_epbc=follow_epbc)
[docs] 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)
[docs] def set_data(self, data, step=0, ignore_unknown=False):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : dict
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)
[docs] def init_state(self, vec=None):
self.variables.init_state(vec=vec)
[docs] def apply_ebc(self, vec=None, force_values=None):
"""
Apply essential (Dirichlet) boundary conditions to equations' variables,
or a given vector.
"""
self.variables.apply_ebc(vec=vec, force_values=force_values)
[docs] def apply_ic(self, vec=None, force_values=None):
"""
Apply initial conditions to equations' variables, or a given vector.
"""
self.variables.apply_ic(vec=vec, force_values=force_values)
[docs] def set_state(self, vec, reduced=False, force=False, preserve_caches=False):
self.variables.set_state(vec, reduced=reduced, force=force,
preserve_caches=preserve_caches)
[docs] def get_lcbc_operator(self):
return self.variables.get_lcbc_operator()
[docs] def evaluate(self, names=None, mode='eval', dw_mode='vector',
term_mode=None, diff_vars=None, asm_obj=None):
"""
Evaluate the equations.
Parameters
----------
names : str or sequence of str, optional
Evaluate only equations of the given name(s).
mode : one of 'eval', 'el_avg', 'qp', 'weak'
The evaluation mode.
dw_mode : one of 'vector', 'matrix', 'sensitivity'
The particular evaluation mode if `mode` is ``'weak'``.
term_mode : str
The term evaluation mode, used mostly if `mode` is ``'eval'`` in
some terms.
diff_vars : list of str
The names of parameters with respect to the equations are
differentiated if `dw_mode` is ``'sensitivity'``.
asm_obj : ndarray or spmatrix
The object for storing the evaluation result in the ``'weak'`` mode.
Returns
-------
out : dict or result
The evaluation result. In 'weak' mode it is the
`asm_obj`. Otherwise, it is a dict of results with equation names
as keys or a single result for a single equation.
"""
if names is None:
eqs = self
single = (len(eqs) == 1)
else:
single = isinstance(names, str)
if single:
names = [names]
eqs = [self[eq] for eq in names]
if mode == 'weak':
extras = []
for eq in eqs:
out = eq.evaluate(mode=mode, dw_mode=dw_mode,
term_mode=term_mode, diff_vars=diff_vars,
asm_obj=asm_obj)
if isinstance(out, tuple): extras.extend(out[1])
out = asm_obj
for extra in extras:
out = out + extra
else:
out = {}
for eq in eqs:
eout = eq.evaluate(mode=mode, dw_mode=dw_mode,
term_mode=term_mode)
out[eq.name] = eout
if single:
out = out.popitem()[1]
return out
[docs] 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_state(state, force=True)
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, reduced=True, allow_dual=True)
residual = self.create_reduced_vec()
eq.evaluate(mode='weak', dw_mode='vector', asm_obj=residual)
out[key] = residual[ir]
else:
out = self.create_reduced_vec()
self.evaluate(mode='weak', dw_mode='vector', asm_obj=out)
return out
[docs] 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_state(state, force=True)
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, reduced=True, allow_dual=True)
ic = get_indx(cname, reduced=True, allow_dual=True)
tangent_matrix.data[:] = 0.0
aux = eq.evaluate(mode='weak', dw_mode='matrix',
asm_obj=tangent_matrix)
out[key] = aux[ir, ic]
else:
tangent_matrix.data[:] = 0.0
out = self.evaluate(mode='weak', dw_mode='matrix',
asm_obj=tangent_matrix)
return out
[docs]class Equation(Struct):
[docs] @staticmethod
def from_desc(name, desc, variables, regions, materials, integrals,
user=None, eterm_options=None, allow_derivatives=False):
term_descs = parse_definition(desc)
terms = Terms.from_desc(term_descs, regions, integrals)
terms.setup(allow_derivatives=allow_derivatives)
terms.assign_args(variables, materials, user)
if eterm_options is not None:
for term in terms:
if isinstance(term, ETermBase):
term.set_verbosity(eterm_options.get('verbosity', 0))
term.set_backend(**eterm_options.get('backend_args', {}))
obj = Equation(name, terms, setup=False)
return obj
def __init__(self, name, terms, setup=True):
Struct.__init__(self, name=name)
if isinstance(terms, Term): # A single term.
terms = Terms([terms])
self.terms = terms
if setup:
self.terms.setup()
[docs] def collect_materials(self):
"""
Collect materials present in the terms of the equation.
"""
materials = []
for term in self.terms:
materials.extend(term.get_materials(join=True))
return materials
[docs] def collect_variables(self):
"""
Collect variables present in the terms of the equation.
Ensures that corresponding primary variables of test/parameter
variables are always in the list, even if they are not directly
used in the terms.
"""
variables = []
for term in self.terms:
var_names = term.get_variable_names()
aux = term.get_args_by_name(var_names)
for var in aux:
variables.append(var)
pvar = var.get_primary()
if pvar is not None:
variables.append(pvar)
return variables
[docs] def collect_conn_info(self, conn_info):
for term in self.terms:
key = (self.name,) + term.get_conn_key()
conn_info[key] = term.get_conn_info()
[docs] def evaluate(self, mode='eval', dw_mode='vector', term_mode=None,
diff_vars=None, asm_obj=None):
"""
Evaluate the equation.
Parameters
----------
mode : one of 'eval', 'el_eval', 'el_avg', 'qp', 'weak'
The evaluation mode.
dw_mode : one of 'vector', 'matrix', 'sensitivity'
The particular evaluation mode if `mode` is ``'weak'``.
term_mode : str
The term evaluation mode, used mostly if `mode` is ``'eval'`` in
some terms.
diff_vars : list of str
The names of parameters with respect to the equation is
differentiated if `dw_mode` is ``'sensitivity'``.
asm_obj : ndarray or spmatrix
The object for storing the evaluation result in the ``'weak'`` mode.
Returns
-------
out : result
The evaluation result. In 'weak' mode it is the
`asm_obj`.
"""
if mode in ('eval', 'el_eval', 'el_avg', 'qp'):
val = 0.0
for term in self.terms:
aux, status = term.evaluate(mode=mode,
term_mode=term_mode,
standalone=False,
ret_status=True)
val += aux
out = val
elif mode == 'weak':
if dw_mode == 'vector':
for term in self.terms:
val, iels, status = term.evaluate(mode=mode,
term_mode=term_mode,
standalone=False,
ret_status=True)
term.assemble_to(asm_obj, val, iels, mode=dw_mode)
out = asm_obj
elif dw_mode == 'matrix':
extras = []
for term in self.terms:
svars = term.get_state_variables(unknown_only=True)
for svar in svars:
val, iels, status = term.evaluate(mode=mode,
term_mode=term_mode,
diff_var=svar.name,
standalone=False,
ret_status=True)
extra = term.assemble_to(asm_obj, val, iels,
mode=dw_mode, diff_var=svar)
if extra is not None: extras.append(extra)
out = (asm_obj, extras) if len(extras) else asm_obj
elif dw_mode == 'sensitivity':
# Differentiation w.r.t. material parameters.
if diff_vars is None: diff_vars = ()
for ic, diff_var in enumerate(diff_vars):
for term in self.terms:
if not (term.diff_info and
(diff_var in term.get_material_names(part=1))):
continue
val, iels, status = term.evaluate(mode=mode,
term_mode=term_mode,
diff_var=diff_var,
standalone=False,
ret_status=True)
term.assemble_to(asm_obj[:, ic], val, iels)
out = asm_obj
else:
raise ValueError('unknown assembling mode! (%s)' % dw_mode)
else:
raise ValueError('unknown evaluation mode! (%s)' % mode)
return out