Source code for sfepy.discrete.common.region

from __future__ import absolute_import
import re
from copy import copy

import numpy as nm

from sfepy.base.base import assert_, Struct
import six
from six.moves import range

_depends = re.compile('r\.([a-zA-Z_\-0-9.]+)').findall

[docs]def get_parents(selector): """ Given a region selector, return names of regions it is based on. """ parents = _depends(selector) return parents
[docs]def get_dependency_graph(region_defs): """ Return a dependency graph and a name-sort name mapping for given region definitions. """ graph = {} name_to_sort_name = {} for sort_name, rdef in six.iteritems(region_defs): name, sel = rdef.name, rdef.select if name in name_to_sort_name: msg = 'region %s/%s already defined!' % (sort_name, name) raise ValueError(msg) name_to_sort_name[name] = sort_name if name not in graph: graph[name] = [0] for parent in get_parents(sel): graph[name].append(parent) if rdef.get('parent', None) is not None: graph[name].append(rdef.parent) return graph, name_to_sort_name
[docs]def sort_by_dependency(graph): out = [] n_nod = len(graph) idone = 0 idone0 = -1 while idone < n_nod: dep_removed = 0 for node, deps in six.iteritems(graph): if (len(deps) == 1) and not deps[0]: out.append(node) deps[0] = 1 idone += 1 elif not deps[0]: for ii, dep in enumerate(deps[1:]): if not dep in graph: msg = 'dependency %s of region %s does not exist!' raise ValueError(msg % (dep, node)) if graph[dep][0]: ir = deps.index(dep) deps.pop(ir) dep_removed += 1 if (idone <= idone0) and not dep_removed: raise ValueError('circular dependency') idone0 = idone return out
[docs]def are_disjoint(r1, r2): """ Check if the regions `r1` and `r2` are disjoint. Uses vertices for the check - `*_only` regions not allowed. """ return len(nm.intersect1d(r1.vertices, r2.vertices, assume_unique=True)) == 0
def _join(def1, op, def2): return '(' + def1 + ' ' + op + ' ' + def2 + ')'
[docs]class Region(Struct): """ Region defines a subset of a FE domain. Region kinds: - cell_only, facet_only, face_only, edge_only, vertex_only - only the specified entities are included, others are empty sets (so that the operators are still defined) - cell, facet, face, edge, vertex - entities of higher dimension are not included The 'cell' kind is the most general and it is the default. Region set-like operators: + (union), - (difference), * (intersection), followed by one of ('v', 'e', 'f', 'c', and 's') for vertices, edges, faces, cells, and facets. Created: 31.10.2005 """ __can = { 'cell' : (1, 1, 1, 1), 'face' : (1, 1, 1, 0), 'edge' : (1, 1, 0, 0), 'vertex' : (1, 0, 0, 0), 'cell_only' : (0, 0, 0, 1), 'face_only' : (0, 0, 1, 0), 'edge_only' : (0, 1, 0, 0), 'vertex_only' : (1, 0, 0, 0), } __facet_kinds = { 1 : {'facet' : 'vertex', 'facet_only' : 'vertex_only'}, 2 : {'facet' : 'edge', 'facet_only' : 'edge_only'}, 3 : {'facet' : 'face', 'facet_only' : 'face_only'}, } __op_to_fun = { '+' : nm.union1d, '-' : nm.setdiff1d, '*' : nm.intersect1d, }
[docs] @staticmethod def from_vertices(vertices, domain, name='region', kind='cell'): """ Create a new region containing given vertices. Parameters ---------- vertices : array The array of vertices. domain : Domain instance The domain containing the vertices. name : str, optional The name of the region. kind : str, optional The kind of the region. Returns ------- obj : Region instance The new region. """ obj = Region(name, 'given vertices', domain, '', kind=kind) obj.vertices = vertices return obj
[docs] @staticmethod def from_facets(facets, domain, name='region', kind='facet', parent=None): """ Create a new region containing given facets. Parameters ---------- facets : array The array with indices to unique facets. domain : Domain instance The domain containing the facets. name : str, optional The name of the region. kind : str, optional The kind of the region. parent : str, optional The name of the parent region. Returns ------- obj : Region instance The new region. """ obj = Region(name, 'given faces', domain, '', kind=kind, parent=parent) obj.facets = facets return obj
[docs] @staticmethod def from_cells(cells, domain, name='region', kind='cell', parent=None): """ Create a new region containing given cells. Parameters ---------- cells : array The array of cells. domain : Domain instance The domain containing the facets. name : str, optional The name of the region. kind : str, optional The kind of the region. parent : str, optional The name of the parent region. Returns ------- obj : Region instance The new region. """ obj = Region(name, 'given cells', domain, '', kind=kind, parent=parent) obj.cells = cells return obj
def __init__(self, name, definition, domain, parse_def, kind='cell', parent=None): """ Create region instance. Parameters ---------- name : str The region name, either given, or automatic for intermediate regions. definition : str The region selector definition. domain : Domain instance The domain of the region. parse_def : str The parsed definition of the region. kind : str The region kind - one of 'cell', 'facet', 'face', 'edge', 'vertex', 'cell_only', ..., 'vertex_only'. parent : str, optional The name of the parent region. """ tdim = domain.shape.tdim Struct.__init__(self, name=name, definition=definition, domain=domain, parse_def=parse_def, n_v_max=domain.shape.n_nod, dim=domain.shape.dim, tdim=tdim, kind_tdim=None, entities=[None] * (tdim + 1), kind=None, parent=parent, shape=None, mirror_regions={}, mirror_maps={}, is_empty=False) self.set_kind(kind)
[docs] def set_kind(self, kind): if kind == self.kind: return self.kind = kind if 'facet' in kind: self.true_kind = self.__facet_kinds[self.tdim][kind] else: self.true_kind = kind can = [bool(ii) for ii in self.__can[self.true_kind]] self.can_vertices = can[0] if self.tdim == 1: self.can = (can[0], can[3]) self.can_cells = can[1] elif self.tdim == 2: self.can = (can[0], can[1], can[3]) self.can_edges = can[1] self.can_cells = can[2] else: self.can = can self.can_edges = can[1] self.can_faces = can[2] self.can_cells = can[3] for ii, ican in enumerate(self.can): if not ican: self.entities[ii] = nm.empty(0, dtype=nm.uint32) self.set_kind_tdim()
[docs] def set_kind_tdim(self): if 'vertex' in self.true_kind: self.kind_tdim = 0 elif 'edge' in self.true_kind: self.kind_tdim = 1 elif 'face' in self.true_kind: self.kind_tdim = 2 elif 'cell' in self.true_kind: self.kind_tdim = self.tdim
@property def vertices(self): if self.entities[0] is None: self._access(1) self.setup_from_highest(0) return self.entities[0] @vertices.setter def vertices(self, vals): if self.can_vertices: self.entities[0] = nm.asarray(vals, dtype=nm.uint32) else: raise ValueError('region "%s" cannot have vertices!' % self.name) @property def edges(self): if self.tdim <= 1: raise AttributeError('1D region has no edges!') if self.entities[1] is None: if 'edge' in self.true_kind: self.setup_from_vertices(1) else: self._access(2) self.setup_from_highest(1) return self.entities[1] @edges.setter def edges(self, vals): if self.can_edges: self.entities[1] = nm.asarray(vals, dtype=nm.uint32) else: raise ValueError('region "%s" cannot have edges!' % self.name) @property def faces(self): if self.tdim <= 2: raise AttributeError('1D or 2D region has no faces!') if self.entities[2] is None: if 'face' in self.true_kind: self.setup_from_vertices(2) else: self._access(3) self.setup_from_highest(2) return self.entities[2] @faces.setter def faces(self, vals): if self.can_faces: self.entities[2] = nm.asarray(vals, dtype=nm.uint32) else: raise ValueError('region "%s" cannot have faces!' % self.name) @property def facets(self): if self.tdim == 3: return self.faces elif self.tdim == 2: return self.edges else: return self.vertices @facets.setter def facets(self, vals): if self.tdim == 3: self.faces = vals elif self.tdim == 2: self.edges = vals else: self.vertices = vals @property def cells(self): if self.entities[self.tdim] is None: self.setup_from_vertices(self.tdim) return self.entities[self.tdim] @cells.setter def cells(self, vals): if self.can_cells: self.entities[self.tdim] = nm.asarray(vals, dtype=nm.uint32) else: raise ValueError('region "%s" cannot have cells!' % self.name) def _access(self, dim): """ Helper to access region entities of dimension `dim`. """ if dim == 0: self.vertices elif dim == 1: if self.tdim == 1: self.cells else: self.edges elif dim == 2: if self.tdim == 3: self.faces else: self.cells else: self.cells
[docs] def setup_from_highest(self, dim, allow_lower=True, allow_empty=False): """ Setup entities of topological dimension `dim` using the available entities of the highest topological dimension. """ if not self.can[dim]: return for idim in range(self.tdim, -1, -1): if self.entities[idim] is not None: if self.entities[idim].shape[0] > 0: break else: if not (allow_empty or self.is_empty): msg = 'region "%s" has no entities!' raise ValueError(msg % self.name) if self.entities[dim] is None: self.entities[dim] = nm.empty(0, dtype=nm.uint32) self.is_empty = True return cmesh = self.domain.cmesh if idim <= dim: if not (allow_lower or allow_empty): msg = 'setup_from_highest() can be used only with dim < %d' raise ValueError(msg % idim) if allow_lower: cmesh.setup_connectivity(dim, idim) ents = self.get_entities(idim) self.entities[dim] = cmesh.get_complete(dim, ents, idim) else: for idim in range(self.kind_tdim - 1, -1, -1): self.entities[idim] = nm.empty(0, dtype=nm.uint32) self.is_empty = True else: cmesh.setup_connectivity(idim, dim) incident = cmesh.get_incident(dim, self.entities[idim], idim) self.entities[dim] = nm.unique(incident)
[docs] def setup_from_vertices(self, dim): """ Setup entities of topological dimension `dim` using the region vertices. """ if not self.can[dim]: return cmesh = self.domain.cmesh cmesh.setup_connectivity(dim, 0) vv = self.vertices self.entities[dim] = cmesh.get_complete(dim, vv, 0)
[docs] def finalize(self, allow_empty=False): """ Initialize the entities corresponding to the region kind and regenerate all already existing (accessed) entities of lower topological dimension from the kind entities. """ self._access(self.kind_tdim) is_empty = self.entities[self.kind_tdim].shape[0] == 0 if allow_empty: self.is_empty = is_empty elif is_empty: raise ValueError('region "%s" has no entities!' % self.name) for idim in range(self.kind_tdim - 1, -1, -1): if self.can[idim] and self.entities[idim] is not None: try: self.setup_from_highest(idim, allow_lower=False, allow_empty=allow_empty) except ValueError as exc: msg = '\n'.join((str(exc), 'fix region kind? (region: %s, kind: %s)' % (self.name, self.kind))) raise ValueError(msg)
[docs] def eval_op_vertices(self, other, op): parse_def = _join(self.parse_def, '%sv' % op, other.parse_def) tmp = self.light_copy('op', parse_def) tmp.vertices = self.__op_to_fun[op](self.vertices, other.vertices) return tmp
[docs] def eval_op_edges(self, other, op): parse_def = _join(self.parse_def, '%se' % op, other.parse_def) tmp = self.light_copy('op', parse_def) tmp.edges = self.__op_to_fun[op](self.edges, other.edges) return tmp
[docs] def eval_op_faces(self, other, op): parse_def = _join(self.parse_def, '%sf' % op, other.parse_def) tmp = self.light_copy('op', parse_def) tmp.faces = self.__op_to_fun[op](self.faces, other.faces) return tmp
[docs] def eval_op_facets(self, other, op): parse_def = _join(self.parse_def, '%ss' % op, other.parse_def) tmp = self.light_copy('op', parse_def) tmp.facets = self.__op_to_fun[op](self.facets, other.facets) return tmp
[docs] def eval_op_cells(self, other, op): parse_def = _join(self.parse_def, '%sc' % op, other.parse_def) tmp = self.light_copy('op', parse_def) tmp.cells = self.__op_to_fun[op](self.cells, other.cells) return tmp
[docs] def light_copy(self, name, parse_def): return Region(name, self.definition, self.domain, parse_def, kind=self.kind)
[docs] def copy(self): """ Vertices-based copy. """ tmp = self.light_copy('copy', self.parse_def) tmp.vertices = copy(self.vertices) return tmp
[docs] def delete_zero_faces(self, eps=1e-14): raise NotImplementedError
[docs] def update_shape(self): """ Update shape of each group according to region vertices, edges, faces and cells. """ n_vertex = self.vertices.shape[0] n_cell = self.cells.shape[0] n_edge = self.edges.shape[0] if self.tdim > 1 else 0 n_face = self.faces.shape[0] if self.tdim == 3 else 0 n_facet = self.facets.shape[0] if self.tdim > 1 else 0 self.shape = Struct(n_vertex=n_vertex, n_edge=n_edge, n_face=n_face, n_facet=n_facet, n_cell=n_cell)
[docs] def get_entities(self, dim): """ Return mesh entities of dimension `dim`. """ if dim <= self.tdim: self._access(dim) out = self.entities[dim] else: out = nm.empty(0, dtype=nm.uint32) return out
[docs] def get_cells(self, true_cells_only=True): """ Get cells of the region. Raises ValueError if `true_cells_only` is True and the region kind does not allow cells. For `true_cells_only` equal to False, cells incident to facets are returned if the region itself contains no cells. Obeys parent region, if given. """ if self.cells.shape[0] == 0: if true_cells_only: msg = 'region %s has not true cells! (has kind: %s)' \ % (self.name, self.kind) raise ValueError(msg) else: # Has to be consistent with get_facet_indices()! cmesh = self.domain.cmesh cmesh.setup_connectivity(self.tdim - 1, self.tdim) out = cmesh.get_incident(self.tdim, self.facets, self.tdim - 1) if self.parent is not None: pcells = self.domain.regions[self.parent].cells ip = nm.in1d(out, pcells, assume_unique=False) out = out[ip] else: out = self.cells return out
[docs] def get_cell_indices(self, cells, true_cells_only=True): """ Return indices of `cells` in the region cells. Raises ValueError if `true_cells_only` is True and the region kind does not allow cells. For `true_cells_only` equal to False, cells incident to facets are returned if the region itself contains no cells. Notes ----- If the number of unique values in `cells` is smaller or equal to the number of cells in the region, all `cells` has to be also the region cells (`self` is a superset of `cells`). The region cells are considered depending on `true_cells_only`. Otherwise, indices of all cells in `self` that are in `cells` are returned. """ fcells = self.get_cells(true_cells_only=true_cells_only) if len(nm.unique(cells)) <= len(nm.unique(fcells)): # self is a superset of cells. ii = nm.searchsorted(fcells, cells) assert_((fcells[ii] == cells).all()) else: aux = nm.searchsorted(cells, fcells) ii = nm.where(nm.take(cells, aux, mode='clip') == fcells)[0] return ii
[docs] def get_facet_indices(self): """ Return an array (per group) of (iel, ifa) for each facet. A facet can be in 1 (surface) or 2 (inner) cells. """ cmesh = self.domain.cmesh cmesh.setup_connectivity(self.tdim - 1, self.tdim) facets = self.facets cells, offs = cmesh.get_incident(self.tdim, facets, self.tdim - 1, ret_offsets=True) if self.parent is not None: pcells = self.domain.regions[self.parent].cells ip = nm.in1d(cells, pcells, assume_unique=False) cells = cells[ip] counts = nm.diff(offs).astype(nm.int32) pos = nm.repeat(nm.arange(facets.shape[0], dtype=nm.int32), counts) new_counts = nm.bincount(pos, weights=ip).astype(nm.uint32) offs = nm.cumsum(nm.r_[0, new_counts], dtype=nm.uint32) ii = cmesh.get_local_ids(facets, self.tdim - 1, cells, offs, self.tdim) fis = nm.c_[cells, ii] return fis
[docs] def setup_mirror_region(self, mirror_name=None, ret_name=False): """ Find the corresponding mirror region, set up element mapping. """ from sfepy.discrete.fem.mesh import find_map regions = self.domain.regions eopts = self.extra_options if (mirror_name is None) and (eopts is not None)\ and ('mirror_region' in eopts): mirror_name = eopts['mirror_region'] if mirror_name is not None: if mirror_name in self.mirror_regions: return mreg = regions[mirror_name] if self.vertices.shape[0] != mreg.vertices.shape[0]: raise ValueError('%s: incompatible mirror region! (%s)' % (self.name, mreg.name)) coors = self.domain.cmesh.coors coors1 = coors[self.vertices, :] coors2 = coors[mreg.vertices, :] shift = ((nm.sum(coors2, axis=0) - nm.sum(coors1, axis=0)) / coors1.shape[0]) vmap1, vmap2 = find_map(coors1, coors2 - shift, join=False) if vmap1.shape[0] != coors1.shape[0]: print(coors1[vmap1]) print(coors2[vmap2]) raise ValueError('cannot match vertices!') fconn = self.domain.cmesh.get_conn_as_graph(self.dim - 1, 0) cc = self.domain.cmesh.get_centroids(self.dim - 1) fmap1, fmap2 = find_map(cc[self.facets], cc[mreg.facets] - shift, join=False) if fmap1.shape[0] != self.facets.shape[0]: print(cc[self.facets][fmap1]) print(cc[mreg.facets][fmap2]) raise ValueError('cannot match facets!') mirror_map_i = nm.zeros_like(fmap1) mirror_map_i[fmap1] = fmap2 mirror_map = nm.zeros_like(fmap1) mirror_map[fmap2] = fmap1 else: for reg in regions: mirror_parent = regions.find(reg.parent) if mirror_parent is None: continue if ((reg is not self) and nm.all(self.vertices == reg.vertices)): mreg = reg mirror_map = mirror_map_i = None break else: raise ValueError('cannot find mirror region! (%s)' % self.name) self.mirror_regions[mreg.name] = mreg self.mirror_maps[mreg.name] = mirror_map mreg.mirror_regions[self.name] = self mreg.mirror_maps[self.name] = mirror_map_i if ret_name: return mreg.name
[docs] def get_mirror_region(self, name): return self.mirror_regions[name]
[docs] def get_n_cells(self, is_surface=False): """ Get number of region cells. Parameters ---------- is_surface : bool If True, number of edges or faces according to domain dimension is returned instead. Returns ------- n_cells : int The number of cells. """ if is_surface: return self.shape.n_facet else: return self.shape.n_cell
[docs] def has_cells(self): return self.cells.size > 0
[docs] def contains(self, other): """ Return True in the region contains the `other` region. The check is performed using entities corresponding to the other region kind. """ tdim = other.kind_tdim se = self.get_entities(tdim) oe = other.entities[tdim] return len(nm.intersect1d(se, oe))
[docs] def get_charfun(self, by_cell=False, val_by_id=False): """ Return the characteristic function of the region as a vector of values defined either in the mesh vertices (by_cell == False) or cells. The values are either 1 (val_by_id == False) or sequential id + 1. """ if by_cell: chf = nm.zeros((self.domain.shape.n_el,), dtype=nm.float64) if val_by_id: chf[self.cells] = self.cells + 1 else: chf[self.cells] = 1.0 else: chf = nm.zeros((self.domain.shape.n_nod,), dtype=nm.float64) if val_by_id: chf[self.vertices] = self.vertices + 1 else: chf[self.vertices] = 1.0 return chf
[docs] def get_edge_graph(self): """ Return the graph of region edges as a sparse matrix having uid(k) + 1 at (i, j) if vertex[i] is connected with vertex[j] by the edge k. Degenerate edges are ignored. """ from scipy.sparse import csr_matrix cmesh = self.domain.cmesh e_verts = cmesh.get_incident(0, self.edges, 1) e_verts.shape = (e_verts.shape[0] // 2, 2) ii = nm.where(e_verts[:, 0] != e_verts[:, 1])[0] edges = self.edges[ii] e_verts = e_verts[ii] vals = edges + 1 rows = e_verts[:, 0] cols = e_verts[:, 1] num = self.vertices.max() + 1 graph = csr_matrix((vals, (rows, cols)), shape=(num, num)) nnz = graph.nnz # Symmetrize. graph = graph + graph.T assert_(graph.nnz == 2 * nnz) return graph