Source code for sfepy.discrete.equations

"""
Classes of equations composed of terms.
"""
from __future__ import absolute_import
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
import six

[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, verbose=True): objs = OneTypeList(Equation) conf = copy(conf) ii = 0 for name, desc in six.iteritems(conf): 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) 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 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. 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 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', 'custom') 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() rname = rvar.get_primary_name() rkey = (rname, rreg_name, dct, False) ckey = (cvar.name, creg_name, dct, info.is_trace) dc_key = (rkey, ckey) if not dc_key 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 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. 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) 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, 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, float(nnz) / nm.prod(shape)), 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_state_vector(self): return self.variables.create_state_vector()
[docs] def create_stripped_state_vector(self): return self.variables.create_stripped_state_vector()
[docs] 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)
[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_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)
[docs] 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)
[docs] 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)
[docs] 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)
[docs] def apply_ic(self, vec, force_values=None): """ Apply initial conditions to a state vector. """ self.variables.apply_ic(vec, force_values=force_values)
[docs] 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)
[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, asm_obj=None): """ Evaluate the equations. Parameters ---------- mode : one of 'eval', 'el_avg', 'qp', 'weak' The evaluation mode. names : str or sequence of str, optional Evaluate only equations of the given name(s). 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, 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_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
[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_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 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): term_descs = parse_definition(desc) terms = Terms.from_desc(term_descs, regions, integrals) terms.setup() terms.assign_args(variables, materials, user) obj = Equation(name, terms) return obj
def __init__(self, name, terms): Struct.__init__(self, name=name) if isinstance(terms, Term): # A single term. terms = Terms([terms]) self.terms = terms 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, asm_obj=None): """ Parameters ---------- mode : one of 'eval', 'el_eval', 'el_avg', 'qp', 'weak' The evaluation mode. """ 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 else: raise ValueError('unknown assembling mode! (%s)' % dw_mode) else: raise ValueError('unknown evaluation mode! (%s)' % mode) return out