from __future__ import absolute_import
import re
import numpy as nm
from sfepy.base.base import assert_, Struct
_depends = re.compile(r'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 region_defs.items():
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 graph.items():
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, tdim=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 : int
The topological dimension of the cells.
"""
if tdim is None:
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,
cmesh=domain.cmesh_tdim[tdim])
self.set_kind(kind)
[docs] def set_kind(self, kind):
if kind == self.kind: return
if self.__facet_kinds[self.tdim]['facet'] == kind:
kind = 'facet'
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]
self.can_cells = can[3]
if self.tdim == 1:
self.can = (can[0], can[3])
self.can_edges = False
self.can_faces = False
elif self.tdim == 2:
self.can = (can[0], can[1], can[3])
self.can_edges = can[1]
self.can_faces = False
else:
self.can = can
self.can_edges = can[1]
self.can_faces = can[2]
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.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.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, tdim=self.tdim)
tmp.cells = self.__op_to_fun[op](self.cells, other.cells)
return tmp
[docs] def light_copy(self, name, parse_def, tdim=None):
return Region(name, self.definition, self.domain, parse_def,
kind=self.kind, tdim=tdim)
[docs] def copy(self):
"""
Make a copy based on the region kind.
"""
tmp = self.light_copy('copy', self.parse_def, tdim=self.tdim)
tmp.entities[self.kind_tdim] = self.get_entities(self.kind_tdim).copy()
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]
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.kind != 'cell':
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.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.
Raises ValueError if all `cells` are not in the region cells.
"""
fcells = self.get_cells(true_cells_only=true_cells_only)
iin = nm.isin(cells, fcells)
if not iin.all():
raise ValueError(f'some cells are not in region {self.name} cells!')
iis = nm.searchsorted(fcells, cells)
assert_((fcells[iis[iin]] == cells[iin]).all())
ii = nm.where(iin, iis, -1)
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.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 mirror_name if ret_name else None
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.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!')
_ = self.cmesh.get_conn_as_graph(self.dim - 1, 0)
cc1 = self.cmesh.get_centroids(self.dim - 1)
sfacets = self.cells if self.tdim < self.dim else self.facets
cc2 = mreg.cmesh.get_centroids(mreg.dim - 1)
mfacets = mreg.cells if mreg.tdim < mreg.dim else mreg.facets
fmap1, fmap2 = find_map(cc1[sfacets], cc2[mfacets] - shift,
join=False)
if fmap1.shape[0] != sfacets.shape[0]:
print(cc1[sfacets][fmap1])
print(cc2[mfacets][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.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