Source code for connectivity

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"""A class and functions for handling nodal connectivity.

This module defines a specialized array class for representing nodal
connectivity. This is e.g. used in mesh models, where geometry is
represented by a set of numbered points (nodes) and the geometric elements
are described by refering to the node numbers.
In a mesh model, points common to adjacent elements are unique, and
adjacency of elements can easily be detected from common node numbers.
from __future__ import absolute_import, division, print_function

from itertools import combinations
import numpy as np

from pyformex import utils
from pyformex import arraytools as at
from pyformex.adjacency import Adjacency

##   class Connectivity

[docs]class Connectivity(np.ndarray): # # :DEV # Because we have a __new__ constructor and no __init__, # we have to put the signature of the object creation explicitely # in the first line of the docstring. # """Connectivity(data=[],dtyp=None,copy=False,nplex=0,eltype=None) A class for handling element to node connectivity. A connectivity object is a 2-dimensional integer array with all non-negative values. Each row of the array defines an element by listing the numbers of its lower entity types. A typical use is a :class:`~mesh.Mesh` object, where each element is defined in function of its nodes. While in a Mesh the word 'node' will normally refer to a geometrical point, here we will use 'node' for the lower entity whatever its nature is. It doesn't even have to be a geometrical entity. Note ---- The current implementation limits a Connectivity object to numbers that are smaller than 2**31. That is however largely sufficient for all practical cases. In a row (element), the same node number may occur more than once, though usually all numbers in a row are different. Rows containing duplicate numbers are called `degenerate` elements. Rows containing the same node sets, albeit different permutations thereof, are called duplicates. Parameters ---------- data: int :term: Data to initialize the Connectivity. The data should be 2-dim with shape ``(nelems,nplex)``, where ``nelems`` is the number of elements and ``nplex`` is the plexitude of the elements. dtyp: float datatype, optional It not provided, the datatype of ``data`` is used. copy: bool, optional If True, the data are copied. The default setting will try to use the original data if possible, e.g. if ``data`` is a correctly shaped and typed :class:`numpy.ndarray`. nplex: int, optional The plexitude of the data. This can be specified to force a check on the plexitude of the data, or to set the plexitude for an empty Connectivity. If an ``eltype`` is specified, the plexitude of the element type will override this value. eltype: str or :class:`elements.ElementType` subclass, optional The element type associated with the Connectivity. It can be either a subclass of:class:`elements.ElementType` or the ``name`` of such a subclass. If not provided, a non-typed Connectivity will result. If that is used to create a :class:`Mesh`, the proper element type will have to be specified at Mesh creation time. If the Connectivity will be used for other purposes, the element type may not be needed or not be important. Raises ------ ValueError If ``nplex`` is provided and the specified ``data`` do not match the specified plexitude. Notes ----- Empty Connectivities with ``nelems==0`` and ``nplex > 0`` can be useful, but a Connectivity with ``nplex==0`` generally is not. Examples -------- >>> Connectivity([[0,1,2],[0,1,3],[0,3,2],[0,5,3]]) Connectivity([[0, 1, 2], [0, 1, 3], [0, 3, 2], [0, 5, 3]]) >>> Connectivity(np.array([],dtype=at.Int).reshape(0,3)) Connectivity([], shape=(0, 3)) """ _exclude_members_ = ['reorderNodes'] def __new__(self, data=[], dtyp=None, copy=False, nplex=0, eltype=None): """Create a new Connectivity object.""" if isinstance(data, Connectivity): if nplex == 0: nplex = data.nplex() if eltype is None: eltype = data.eltype if eltype is None: try: eltype = data.eltype except: eltype = None # Turn the data into an array, and copy if requested ar = np.array(data, dtype=dtyp, copy=copy) if ar.ndim < 2: if nplex > 0: ar = ar.reshape(-1, nplex) else: ar = ar.reshape(-1, 1) elif ar.ndim > 2: raise ValueError("Expected 2-dim data") # Make sure dtype is an int type if ar.dtype.kind != 'i': ar = ar.astype(at.Int) # Check values if ar.size > 0: if ar.max() >= 2**31 or (ar.min() < 0): raise ValueError("Negative or too large positive value in data") if nplex > 0 and ar.shape[1] != nplex: raise ValueError("Expected data of plexitude %s" % nplex) else: if nplex > 0: ar = ar.reshape(0, nplex) # Transform 'subarr' from an ndarray to our new subclass. ar = ar.view(self) ## # Other data ar.eltype = eltype # ! this may be a string!!!!!!!!!!! ar.inv = None # inverse index ar.eadj = None # element adjacency ar.nadj = None # node adjacency return ar def __array_finalize__(self, obj): # reset the attributes from passed original object # all extra attributes added in __new__ should be reset here self.eltype = getattr(obj, 'eltype', None) self.inv = getattr(obj, 'inv', None) self.eadj = getattr(obj, 'eadj', None) self.nadj = getattr(obj, 'nadj', None) def __reduce__(self): """Reduce the object to a pickled state""" # Get the pickled ndarray state (as a list, so we can change it) object_state = list(np.ndarray.__reduce__(self)) # Define our own state with the extra attributes we added subclass_state = (self.eltype, None) # Store both in place of the original ndarray state object_state[2] = (object_state[2], subclass_state) return tuple(object_state) def __setstate__(self, state): """Restore from pickled state""" # In __reduce__, we replaced ndarray's state with a tuple # of itself and our own state try: nd_state, own_state = state np.ndarray.__setstate__(self, nd_state) self.eltype, self.inv = own_state except: try: # try to read legacy pickle format, which did not save # the element type (rev < 2360) np.ndarray.__setstate__(self, state) print("WARNING: Connectivity was restored without element type!") except: print("I could not unpickle the Connectivity," " neither in old nor new format") raise def __repr__(self): """String representation of a Connectivity Examples -------- >>> Connectivity([[0,1,2],[0,1,3]],eltype='line3') Connectivity([[0, 1, 2], [0, 1, 3]], eltype='line3') """ res = np.ndarray.__repr__(self) # This is not needed for doctests, but is needed for # normal output if self.dtype == at.Int: res = res.replace(', dtype=int32', '') if self.eltype is not None: res = res.replace(')', ", eltype='%s')" % self.eltype) return res
[docs] def nelems(self): """Return the number of elements in the Connectivity table. Returns ------- int The number of rows in the table. Examples -------- >>> Connectivity([[0,1,2],[0,1,3],[0,3,2],[0,5,3]]).nelems() 4 """ return self.shape[0]
[docs] def maxnodes(self): """Return an upper limit for number of nodes in the Connectivity. Returns ------- int The highest node number plus one. See Also -------- nnodes: the actual number of nodes in the table Examples -------- >>> Connectivity([[0,1,2],[0,1,3],[0,3,2],[0,5,3]]).maxnodes() 6 """ return int(self.max() + 1)
[docs] def nnodes(self): """Return the actual number of nodes in the Connectivity. This returns the count of the unique node numbers. See Also -------- maxnodes: the highest node number + 1 Examples -------- >>> Connectivity([[0,1,2],[0,1,3],[0,3,2],[0,5,3]]).nnodes() 5 """ return np.unique(self).shape[0]
[docs] def nplex(self): """Return the plexitude of the elements in the Connectivity table. Examples -------- >>> Connectivity([[0,1,2],[0,1,3],[0,3,2],[0,5,3]]).nplex() 3 """ return self.shape[1]
[docs] def report(self): """Format a Connectivity table""" s = "Connectivity %s, eltype=%s" % (self.shape, self.eltype) return s + '\n' + np.ndarray.__str__(self)
############### Detecting degenerates and duplicates ##############
[docs] def testDegenerate(self): """Flag the degenerate elements (rows). A degenerate element is a row which contains at least two equal values. Returns ------- bool array A 1-dim bool array with length ``self.nelems()``, holding True values for the degenerate rows. Examples -------- >>> Connectivity([[0,1,2],[0,1,1],[0,3,2]]).testDegenerate() array([False, True, False]) """ srt = np.asarray(self.copy()) srt.sort(axis=1) return (srt[:, :-1] == srt[:, 1:]).any(axis=1)
[docs] def listDegenerate(self): """Return a list with the numbers of the degenerate elements. Returns ------- int array A 1-dim int array holding the row indices of the degenerate elements. Examples -------- >>> Connectivity([[0,1,2],[0,1,1],[0,3,2]]).listDegenerate() array([1]) """ return np.arange(self.nelems())[self.testDegenerate()]
[docs] def listNonDegenerate(self): """Return a list with the numbers of the non-degenerate elements. Returns ------- int array A 1-dim int array holding the row indices of the non-degenerate elements. Examples -------- >>> Connectivity([[0,1,2],[0,1,1],[0,3,2]]).listNonDegenerate() array([0, 2]) """ return np.arange(self.nelems())[~self.testDegenerate()]
[docs] def removeDegenerate(self): """Remove the degenerate elements from a Connectivity table. Returns ------- Connectivity A Connectivity object with the degenerate elements removed. Examples -------- >>> Connectivity([[0,1,2],[0,1,1],[0,3,2]]).removeDegenerate() Connectivity([[0, 1, 2], [0, 3, 2]]) """ return self[~self.testDegenerate()]
[docs] def findDuplicate(self, permutations='all'): """Find duplicate rows in the Connectivity. Parameters ---------- permutations: str Defines which permutations of the row data are allowed while still considering the rows equal. Possible values are: - 'none': no permutations are allowed: rows must match the same date at the same positions. - 'roll': rolling is allowed. Rows that can be transformed into each other by rolling are considered equal; - 'all': any permutation of the same data will be considered an equal row. This is the default. Returns ------- V: :class:`~varray.Varray` A Varray where each row contains a list of the row numbers from a that are considered equal. The entries in each row are sorted and the rows are sorted according to their first element. Notes ----- This is like :func:`arraytools.equalRows` but has a different default value for ``permutations``. Examples -------- >>> C = Connectivity([[0,1,2],[0,1,3],[0,1,2],[2,0,1],[2,1,0]]) >>> C.findDuplicate() Varray([[0, 2, 3, 4], [1]]) >>> C.findDuplicate(permutations='roll') Varray([[0, 2, 3], [1], [4]]) >>> C.findDuplicate(permutations='none') Varray([[0, 2], [1], [3], [4]]) """ return at.equalRows(self, permutations=permutations)
[docs] def listDuplicate(self, permutations='all'): """Return a list with the numbers of the duplicate elements. Returns ------- 1-dim int array The indices of the unique rows in the Connectivity array. Examples -------- >>> C = Connectivity([[0,1,2],[0,1,3],[0,1,2],[2,0,1],[2,1,0]]) >>> C.listDuplicate() array([2, 3, 4]) >>> C.listDuplicate(permutations='roll') array([2, 3]) >>> C.listDuplicate(permutations='none') array([2]) """ ind, ok = at.findEqualRows(self, permutations=permutations) return np.sort(ind[~ok])
[docs] def listUnique(self, permutations='all'): """Return a list with the numbers of the unique elements. Returns ------- 1-dim int array The indices of the unique rows in the Connectivity array. See Also -------- findDuplicate: find duplicate rows listDuplicate: list duplicate rows removeDuplicate: remove duplicate rows Examples -------- >>> C = Connectivity([[0,1,2],[0,1,3],[0,1,2],[2,0,1],[2,1,0]]) >>> C.listUnique() array([0, 1]) >>> C.listUnique(permutations='roll') array([0, 1, 4]) >>> C.listUnique(permutations='none') array([0, 1, 3, 4]) """ return at.uniqueRows(self, permutations=permutations)
[docs] def removeDuplicate(self, permutations='all'): """Remove duplicate elements from a Connectivity list. By default, duplicates are elements that consist of the same set of nodes, in any particular order. Setting permutations to 'none' will only remove the duplicate rows that have matching values at matching positions. Returns ------- Connectivity A new Connectivity with the duplicate elements removed. Examples -------- >>> C = Connectivity([[0,1,2],[0,1,3],[0,1,2],[2,0,1],[2,1,0]]) >>> C.removeDuplicate() Connectivity([[0, 1, 2], [0, 1, 3]]) >>> C.removeDuplicate(permutations='roll') Connectivity([[0, 1, 2], [0, 1, 3], [2, 1, 0]]) >>> C.removeDuplicate(permutations='none') Connectivity([[0, 1, 2], [0, 1, 3], [2, 0, 1], [2, 1, 0]]) """ return self[self.listUnique(permutations)]
[docs] def reorder(self, order='nodes'): """Reorder the elements of a Connectivity in a specified order. This does not actually reorder the elements itself, but returns an index with the order of the rows (elements) in the Connectivity table that meets the specified ordering requirements. Parameters ---------- order: str or list of ints Specifies how to reorder the elements. It is either one of the special string values defined below, or else it is an index with length equal to the number of elements. The index should be a permutation of the numbers in ``range(self.nelems()``. Each value gives the number of the old element that should be placed at this position. Thus, the order values are the old element numbers on the position of the new element number. ``order`` can also take one of the following predefined values, resulting in the corresponding renumbering scheme being generated: - 'nodes': the elements are renumbered in order of their appearance in the inverse index, i.e. first are the elements connected to node 0, then the as yet unlisted elements connected to node 1, etc. - 'random': the elements are randomly renumbered. - 'reverse': the elements are renumbered in reverse order. Returns ------- 1-dim int array Int array with a permutation of ``arange(self.nelems()``, such that taking the elements in this order will produce a Connectivity reordered as requested. In case an explicit order was specified as input, this order is returned after checking that it is indeed a permutation of ``range(self.nelems()``. Examples -------- >>> A = Connectivity([[1,2],[2,3],[3,0],[0,1]]) >>> A[A.reorder('reverse')] Connectivity([[0, 1], [3, 0], [2, 3], [1, 2]]) >>> A[A.reorder('nodes')] Connectivity([[0, 1], [3, 0], [1, 2], [2, 3]]) >>> A[A.reorder([2,3,0,1])] Connectivity([[3, 0], [0, 1], [1, 2], [2, 3]]) """ if order == 'nodes': a = np.sort(self, axis=-1) # first sort rows order = at.sortByColumns(a) elif order == 'reverse': order = np.arange(self.nelems()-1, -1, -1) elif order == 'random': order = random.permutation(self.nelems()) else: order = np.asarray(order) if not (order.dtype.kind == 'i' and (np.sort(order) == np.arange(order.size)).all()): raise ValueError("order should be a permutation of range(%s)" % self.nelems()) return order
[docs] def renumber(self, start=0): """Renumber the nodes to a consecutive integer range. The node numbers in the table are changed thus that they form a consecutive integer range starting from the specified value. Parameters ---------- start: int Lowest node number to be used in the renumbered Connectivity. Returns ------- elems: Connectivity The renumbered Connectivity oldnrs: 1-dim int array The sorted list of unique (old) node numbers. The new node numbers are assigned in order of increasing old node numbers, thus the old node number for new node number ``i`` can be found at position ``i - start``. Examples -------- >>> e,n = Connectivity([[0,2],[1,4],[4,2]]).renumber(7) >>> print(e) [[ 7 9] [ 8 10] [10 9]] >>> print(n) [0 1 2 4] Find the old node number of new node 10 >>> n[10-7] 4 """ nodes = np.asarray(np.unique(self)) if nodes.size == 0: elems = self else: old = np.arange(nodes.max()+1) if nodes.shape[0] == old.shape[0]: # we have a consecutive range if nodes[0] == start: # numbering is ok, keep elems = self else: # add the correct offset elems = self + (start-nodes[0]) else: # need to renumber elems = at.inverseUniqueIndex(nodes)[self] + start elems = Connectivity(elems, eltype=self.eltype) return elems, nodes
[docs] def inverse(self, expand=True): """Return the inverse index of a Connectivity table. Returns ------- int array The inverse index of the Connectivity, as computed by :func:`arraytools.inverseIndex`. Examples -------- >>> Connectivity([[0,1,2],[0,1,4],[0,4,2]]).inverse() array([[ 0, 1, 2], [-1, 0, 1], [-1, 0, 2], [-1, -1, -1], [-1, 1, 2]]) >>> Connectivity([[0,1,2],[0,1,4],[0,4,2]]).inverse(expand=False) Varray([[0, 1, 2], [0, 1], [0, 2], [], [1, 2]]) """ if not expand: # we should not store the inverse return at.inverseIndex(self, expand=expand) if self.inv is None or self.flags.writeable: if self.size > 0: self.inv = at.inverseIndex(self, expand=expand) else: self.inv = Connectivity() self.flags.writeable = False return self.inv
[docs] def nParents(self): """Return the number of elements connected to each node. Returns ------- 1-dim int array The number of elements connected to each node. The length of the array is equal to the highest node number + 1. Unused node numbers will have a count of zero. Examples -------- >>> Connectivity([[0,1,2],[0,1,4],[0,4,2]]).nParents() array([3, 2, 2, 0, 2]) """ r = self.inverse() return (r>=0).sum(axis=1)
[docs] def connectedTo(self, nodes, return_ncon=False): """Check if the elements are connected to the specified nodes. Parameters ---------- nodes: int or int :term: One or more node numbers to check for connections in the table. return_ncon: bool, optional If True, also return the number of connections for each element. Returns ------- connections: int array The numbers of the elements that contain at least one of the specified nodes. ncon: int array, optional The number of connections for each connected element. This is only provided if ``return_ncon`` is True. Examples -------- >>> A = Connectivity([[0,1,2],[0,1,3],[0,3,2],[1,2,3]]) >>> print(A.connectedTo(2)) [0 2 3] >>> A.connectedTo([0,1,3],True) (array([0, 1, 2, 3]), array([2, 3, 2, 2])) """ nodes = at.checkArray1D(nodes, kind='i') nodes = np.intersect1d(nodes, self) # remove unconnected nodes inv = self.inverse() ad = inv[nodes] ad = ad[ad>=0] # We now have a list of all individual attachements to any of the nodes, # identified by the element number. We count them per element. m, u = at.multiplicity(ad) if return_ncon: return u, m else: return u
[docs] def hits(self, nodes): """Count the nodes from a list connected to the elements. Parameters ---------- nodes: int or list of ints One or more node numbers. Returns ------- int array (nelems,) An int array holding the number of nodes from the specified input that are contained in each of the elements. Notes ----- This information can also be got from meth:`connectedTo`. This method however expands the results to the full element set, making it apt for use in selector expressions like ``self[self.hits(nodes) >= 2]``. Examples -------- >>> A = Connectivity([[0,1,2],[0,1,3],[0,3,2],[1,2,3]]) >>> A.hits(2) array([1, 0, 1, 1]) >>> A.hits([0,1,3]) array([2, 3, 2, 2]) """ u, m = self.connectedTo(nodes, True) res = np.zeros(self.shape[0], dtype=m.dtype) res[u] = m return res
[docs] def adjacency(self, kind='e', mask=None): """Create a table of adjacent items. This creates an element adjacency table or node adjacency table An element `i` is said to be adjacent to element `j`, if the two elements have at least one common node. A node `i` is said to be adjacent to node `j`, if there is at least one element containing both nodes. Parameters ---------- kind: 'e' or 'n' Select element ('e') or node (n') adjacency table. Default is element adjacency. mask: bool array or int index, optional Node selector. If provided (with ``kind=='e'``) this defines by a bool flag array or int index numbers the list of nodes that are to be considered connectors between elements. The default is to consider all nodes as connectors. This option is only useful in the case `kind` == 'e'. If you want to use an element mask for the 'n' case, just apply the (element) mask beforehand by using ``self[mask].adjacency('n')``. Returns ------- :class:`~adjacency.Adjacency` object An Adjacency array with shape (nr,nc), where row `i` holds a sorted list of all the items that are adjacent to item `i`, padded with -1 values to create an equal list length for all items. Examples -------- >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacency('e') Adjacency([[ 1, 2, 3], [-1, 0, 3], [-1, -1, 0], [-1, 0, 1]]) >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacency('e',mask=[1,2,3,5]) Adjacency([[ 2], [-1], [ 0], [-1]]) >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacency('n') Adjacency([[ 1, 2, 5], [-1, 0, 3], [-1, -1, 0], [-1, -1, 1], [-1, -1, -1], [-1, -1, 0]]) >>> Connectivity([[0,1,2],[0,1,3],[2,4,5]]).adjacency('n') Adjacency([[-1, 1, 2, 3], [-1, 0, 2, 3], [ 0, 1, 4, 5], [-1, -1, 0, 1], [-1, -1, 2, 5], [-1, -1, 2, 4]]) >>> Connectivity([[0,1,2],[0,1,3],[2,4,5]])[[0,2]].adjacency('n') Adjacency([[-1, -1, 1, 2], [-1, -1, 0, 2], [ 0, 1, 4, 5], [-1, -1, -1, -1], [-1, -1, 2, 5], [-1, -1, 2, 4]]) >>> Connectivity([[0,1,],[2,3]]).adjacency('e') Adjacency([], shape=(2, 0)) """ adj = getattr(self, kind+'adj') if adj is not None: # We already computed it return adj inv = self.inverse() if kind == 'e': if mask is not None: mask = at.complement(mask, inv.shape[0]) inv[mask] = -1 if self.size <= 4000000: # do in one step adj = _elem_adj(inv, self, True) else: # use multiprocessing adj = _elem_adj_multi(inv, self, nproc=4) maxcols = max([a.shape[1] for a in adj]) adj = [at.growAxis(a, maxcols-a.shape[1], axis=1, fill=-1) for a in adj] adj = np.concatenate(adj, axis=0) elif kind == 'n': adj = np.concatenate([np.where(inv>=0, self[:, i][inv], inv) for i in range(self.nplex())], axis=1) else: raise ValueError("kind should be 'e' or 'n', got %s" % str(kind)) adj = Adjacency(adj) # Store the adjacency, because it is expensive to compute # True for eadj, don'tknow for nadj self.flags.writeable = True setattr(self, kind+'adj', adj) self.flags.writeable = False return adj
[docs] def adjacentElements(self, els, mask=None): """Compute adjacent elements. This creates an element adjacency table or node adjacency table. An element `i` is said to be adjacent to element `j`, if the two elements have at least one common node. A node `i` is said to be adjacent to node `j`, if there is at least one element containing both nodes. Parameters ---------- else: int or list of ints The element number(s) for which to compute the adjacent elements mask: bool array or int index, optional Node selector. If provided (with ``kind=='e'``) this defines by a bool flag array or int index numbers the list of nodes that are to be considered connectors between elements. The default is to consider all nodes as connectors. This option is only useful in the case `kind` == 'e'. If you want to use an element mask for the 'n' case, just apply the (element) mask beforehand by using ``self[mask].adjacency('n')``. Returns ------- :class:`~adjacency.Adjacency` object An Adjacency array with shape (nr,nc), where row `i` holds a sorted list of all the items that are adjacent to item `i`, padded with -1 values to create an equal list length for all items. Examples -------- >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacentElements([0,1,2,3]) array([[ 1, 2, 3], [-1, 0, 3], [-1, -1, 0], [-1, 0, 1]]) >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacentElements([0,1,2]) array([[ 1, 2, 3], [-1, 0, 3], [-1, -1, 0]]) >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacentElements([1,2,3]) array([[ 0, 3], [-1, 0], [ 0, 1]]) >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacentElements([0,2]) array([[ 1, 2, 3], [-1, -1, 0]]) >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacentElements([2]) array([[0]]) >>> Connectivity([[0,1],[0,2],[1,3],[0,5]]).adjacentElements(1) array([[0, 3]]) """ els = at.checkArray1D(els, kind='i') nels = els.shape[0] if nels <= 0: return np.array([], dtype=at.Int) inv = self.inverse() # print(inv) if mask is not None: mask = at.complement(mask, inv.shape[0]) inv[mask] = -1 # print(inv[self[els]]) adj = inv[self[els]].reshape((nels, -1)) adj[adj == els.reshape(nels, -1)] = -1 # remove the element itself adj.sort(axis=1) adj[np.where(adj[:, :-1] == adj[:, 1:])] = -1 # remove duplicate items adj.sort(axis=1) maxc = adj.max(axis=0) # find maximum per column adj = adj[:, maxc>=0] # retain columns with non-negative maximum return adj
### frontal methods ### # TODO: This is still much slower that Adjacency.frontwalk # Maybe we should just remove this (or else implement in C)
[docs] def frontGenerator(self, startat=0, frontinc=1, partinc=1): """Generator function returning the frontal elements. This is a generator function and is normally not used directly, but via the :meth:`frontWalk` method. Parameters: see :meth:`frontWalk`. Returns ------- int array Int array with a value for each element. On the initial call, all values are -1, except for the elements in the initial front, which get a value 0. At each call a new front is created with all the elements that are connected to any of the current front and which have not yet been visited. The new front elements get a value equal to the last front's value plus the ``frontinc``. If the front becomes empty and a new starting front is created, the front value is extra incremented with ``partinc``. Examples -------- >>> C = Connectivity([[2,8,7],[2,3,8],[3,9,8],[4,10,9],[5,6,11], ... [6,12,11]]) >>> C.adjacentElements([0]) array([[1, 2]]) >>> for p in C.frontGenerator(): print(p) [ 0 -1 -1 -1 -1 -1] [ 0 1 1 -1 -1 -1] [ 0 1 1 2 -1 -1] [ 0 1 1 2 4 -1] [0 1 1 2 4 5] >>> A = C.adjacency() >>> for p in A.frontGenerator(): print(p) [ 0 -1 -1 -1 -1 -1] [ 0 1 1 -1 -1 -1] [ 0 1 1 2 -1 -1] [ 0 1 1 2 4 -1] [0 1 1 2 4 5] """ if self.nelems() <= 0: return # Initialize result p = -np.ones((self.nelems()), dtype=at.Int) # Compute inverse once, then lock array self.inv = self.inverse() # Remember current elements front elems = np.clip(np.asarray(startat), 0, self.nelems()) prop = 0 while elems.size > 0: # Store prop value for current elems #at.printar("Elems ",elems) p[elems] = prop yield p prop += frontinc # Determine adjacent elements #nodes = np.unique(np.asarray(self[elems])) #elems = self.connectedTo(nodes) elems = np.unique(self.adjacentElements(elems)) while elems[0] < 0: # There should only be one -1 elems = elems[1:] # Remove already done elems = np.setdiff1d(elems, np.where(p>=0)[0]) if elems.size > 0: continue # No more elements in this part: start a new one elems = np.where(p<0)[0] if elems.size > 0: # Start a new part elems = elems[[0]] prop += partinc
[docs] def frontWalk(self, startat=0, frontinc=1, partinc=1, maxval=-1): """Walks through the elements by their node front. A frontal walk is executed starting from the given element(s). A number of steps is executed, each step advancing the front over a given number of single pass increments. The step number at which an element is reached is recorded and returned. Parameters ---------- startat: int or list of ints Initial element number(s) in the front. frontinc: int Increment for the front number on each frontal step. partinc: int Increment for the front number when the front gets empty and a new part is started. maxval: int Maximum frontal value. If negative (default) the walk will continue until all elements have been reached. If non-negative, walking will stop as soon as the frontal value reaches this maximum. Returns ------- int array An array of ints specifying for each element in which step the element was reached by the walker. Examples -------- >>> C = Connectivity([[2,8,7],[2,3,8],[3,9,8],[4,10,9],[5,6,11], ... [6,12,11]]) >>> print(C.frontWalk()) [0 1 1 2 4 5] """ for p in self.frontGenerator( startat=startat, frontinc=frontinc, partinc=partinc): if maxval >= 0: if p.max() >= maxval: break return p
[docs] def front(self, startat=0, add=False): """Returns the elements of the first node front. Parameters ---------- startat: int or list od ints Element number(s) or a list of element numbers. The list of elements to find the next front for. add: bool, optional If True, the `startat` elements wil be included in the return value. The default (False) will only return the elements in the next front line. Returns ------- int array A list of the elements that are connected to any of the nodes that are part of the startat elements. Notes ----- This is equivalent to the first step of a :func:`frontWalk` with the same startat elements, and could thus also be obtained from ``where(self.frontWalk(startat,maxval=1) == 1)[0]``. Here however another implementation is used, which is more efficient for very large models: it avoids the creation of the large array as returned by frontWalk. Examples -------- >>> C = Connectivity([[2,8,7],[2,3,8],[3,9,8],[4,10,9],[5,6,11], ... [6,12,11]]) >>> print(C.front([2])) [0 1 3] """ nodes = np.unique(np.asarray(self[startat])) front = self.connectedTo(nodes) if not add: front = np.setdiff1d(front, startat) return front
######### Creating intermediate levels ###################
[docs] def selectNodes(self, selector): """Return a :class:`Connectivity` containing subsets of the nodes. Parameters ---------- selector: int :term: An object that can be converted to a 1-dim or 2-dim int array. Examples are a tuple of local node numbers, or a list of such tuples all having the same length. Each row of `selector` holds a list of the local node numbers that should be retained in the new Connectivity table. As an example, if the Connectivity is plex-3 representing triangles, a selector [[0,1],[1,2],[2,0]] would extract the edges of the triangle. Returns ------- :class:`Connectivity` A new Connectivity object with shape ``(self.nelems*selector.nelems,selector.nplex)``. Duplicate elements created by the selector are retained. If the selector has an eltype (for example if it is a Connectivity itself), the returned Connectivity will have the same eltype. Examples -------- >>> Connectivity([[0,1,2],[0,2,1],[0,3,2]]).selectNodes([[0,1],[0,2]]) Connectivity([[0, 1], [0, 2], [0, 2], [0, 1], [0, 3], [0, 2]]) """ sel = Connectivity(selector) if sel.size > 0: lo = Connectivity(self[:, sel].reshape(-1, sel.nplex())) lo.eltype = sel.eltype else: lo = Connectivity(eltype=sel.eltype) return lo
[docs] def insertLevel(self, selector, permutations='all'): """Insert an extra hierarchical level in a Connectivity table. A Connectivity table identifies higher hierarchical entities in function of lower ones. This method inserts an extra level in the hierarchy. For example, if you have volumes defined in function of points, you can insert an intermediate level of edges, or faces. Each element may generate multiple instances of the intermediate level. Parameters ---------- selector: int :term: An object that can be converted to a 1-dim or 2-dim int array. Examples are a tuple of local node numbers, or a list of such tuples all having the same length. Each row of `selector` holds a list of the local node numbers that should be retained in the new Connectivity table. permutations: str Defines which permutations of the row data are allowed while still considering the rows equal. Equal rows in the intermediate level are collapsed into single items. Possible values are: - 'none': no permutations are allowed: rows must match the same date at the same positions. - 'roll': rolling is allowed. Rows that can be transformed into each other by rolling are considered equal; - 'all': any permutation of the same data will be considered an equal row. This is the default. Returns ------- hi: :class:`Connectivity` A Connecivity defining the original elements in function of the intermediate level ones. lo: :class:`Connectivity` A Connectivity defining the intermediate level items in function of the lowest level ones (the original nodes). If the ``selector`` has an ``eltype`` attribute, then ``lo`` will inherit the same ``eltype`` value. The resulting node numbering of the created intermediate entities (the `lo` return value) respects the numbering order of the original elements and the applied the selector, but in case of collapsing duplicate rows, it is undefined which of the collapsed sequences is returned. Because the precise order of the data in the collapsed rows is lost, it is in general not possible to restore the exact original table from the two result tables. See however :meth:`mesh.Mesh.getBorder` for an application where an inverse operation is possible, because the border only contains unique rows. See also :meth:`mesh.Mesh.combine`, which is an almost inverse operation for the general case, if the selector is complete. The resulting rows may however be permutations of the original. Examples -------- >>> Connectivity([[0,1,2],[0,2,1],[0,3,2]]).\ insertLevel([[0,1],[1,2],[2,0]]) (Connectivity([[0, 1, 2], [2, 1, 0], [3, 4, 2]]), Connectivity([[0, 1], [1, 2], [2, 0], [0, 3], [3, 2]])) >>> Connectivity([[0,1,2,3]]).\ insertLevel([[0,1,2],[1,2,3],[0,1,1],[0,0,1],[1,0,0]]) (Connectivity([[0, 1, 2, 2, 2]]), Connectivity([[0, 1, 2], [1, 2, 3], [0, 1, 1]])) """ selector = Connectivity(selector) lo = self.selectNodes(selector) if lo.size > 0: # change the double entries to -1 LO = lo.copy() LO[np.where(LO[:, :-1] == LO[:, 1:])] = -1 uniq, uniqid = at.uniqueRowsIndex(LO, permutations=permutations) hi = Connectivity(uniqid.reshape(-1, selector.nelems())) lo = lo[uniq] else: hi = lo = Connectivity() if hasattr(selector, 'eltype') and selector.eltype is not None: lo.eltype = selector.eltype return hi, lo
# TODO: This is currently far from general!!! # should probably be moved to Mesh/TriSurface if needed there
[docs] def combine(self, lo): """Combine two hierarchical Connectivity levels to a single one. self and lo are two hierarchical Connectivity tables, representing higher and lower level respectively. This means that the elements of self hold numbers which point into lo to obtain the lowest level items. *In the current implementation, the plexitude of lo should be 2!* As an example, in a structure of triangles, hi could represent triangles defined by 3 edges and lo could represent edges defined by 2 vertices. This method will then result in a table with plexitude 3 defining the triangles in function of the vertices. This is the inverse operation of :meth:`insertLevel` with a selector which is complete. The algorithm only works if all node numbers of an element are unique. Examples -------- >>> hi,lo = Connectivity([[0,1,2],[0,2,1],[0,3,2]]).\ insertLevel([[0,1],[1,2],[2,0]]) >>> hi.combine(lo) Connectivity([[0, 1, 2], [0, 2, 1], [0, 3, 2]]) """ lo = Connectivity(lo) if self.shape[1] < 2 or lo.shape[1] != 2: raise ValueError("Can only combine plex>=2 with plex==2") elems = lo[self] elems1 = np.roll(elems, -1, axis=1) for i in range(elems.shape[1]): flags = (elems[:, i, 1] != elems1[:, i, 0]) * (elems[:, i, 1] != elems1[:, i, 1]) elems[flags, i] = np.roll(elems[flags, i], 1, axis=1) return Connectivity(elems[:, :, 0])
[docs] def resolve(self): """Resolve the connectivity into plex-2 connections. Creates a Connectivity table with a plex-2 (edge) connection between any two nodes that are connected to a common element. There is no point in resolving a plexitude 2 structure. Plexitudes lower than 2 can not be resolved. Returns a plex-2 Connectivity with all connections between node pairs. In each element the nodes are sorted. Examples -------- >>> print([ i for i in combinations(range(3),2) ]) [(0, 1), (0, 2), (1, 2)] >>> Connectivity([[0,1,2],[0,2,1],[0,3,2]]).resolve() Connectivity([[0, 1], [0, 2], [0, 3], [1, 2], [2, 3]]) """ ind = [i for i in combinations(range(self.nplex()), 2)] hi, lo = self.insertLevel(ind) lo.sort(axis=1) ind = at.sortByColumns(lo) return lo[ind]
# BV: UNTESTED ! def reorderNodes(schemes, reverse=False): """_Convert Connectivity to/from foreign node numbering schemes. The order in which the element's nodes are numbered internally in pyFormex may be different than the numbering scheme used in external software packages. To allow correct export/import to/from other software, the nodes have to be renumbered. This function provides such a facility. Parameters ---------- schemes: dict A dict having pyFormex element names as keys and the matching nodal permutation arrays as values. The length of the array should match the plexitude of the Connectivity. reverse: bool If True, the conversion is from external to internal. In this case, the Connectivity's eltype is interpreted as the pyFormex target element type (and should be set beforehand). Returns ------- Connectivity If the Connectivity has an element type and `scheme` has a key matching the element's name, a Connectivity with the renumbered elements is returned. - If `reverse` is False (default), the renumbering is done according to the permutation given by the `scheme` value matching the element name and the returned Connectivity will have no element type. - If `reverse` is True, the permutation scheme is reversed prior to using it. The target element type is retained in the returned Connectivity. If the Connectivity has no element type or `scheme` has no matching key, the input Connectivity is returned unchanged. """ if self.eltype is not None: eltype = ElementType(self.eltype) key = if key in scheme: print('key = %s' % key) trl = scheme[key] print('trl = %s' % trl) elems = self[trl] if not reverse: delattr(self, 'eltype') return elems return self
[docs] def sharedNodes(self, elist=None): """Return the list of nodes shared by all elements in elist Parameters ---------- elist: int :term: List of element numbers. If not specified, all elements are considered. Returns ------- int array A 1-dim int array with the list of nodes that are common to all elements in the specified list. This array may be empty. Examples -------- >>> a = Connectivity([[0,1,2],[0,2,1],[0,3,2]]) >>> a.sharedNodes() array([0, 2]) >>> a.sharedNodes([0,1]) array([0, 1, 2]) """ if elist is None: elems = self else: elems = self[elist] m, u = at.multiplicity(elems.ravel()) return u[m==len(elems)]
[docs] def replic(self, n, inc): """Repeat a Connectivity with increasing node numbers. Parameters ---------- n: int Number of copies to make. inc: int Increment in node numbers for each copy. Returns ------- Connectivity A Connectivity with the concatenation of ``n`` replicas of ``self``, where the first replica is identical to self and each next one has its node numbers increased by ``inc``. Examples -------- >>> Connectivity([[0,1,2],[0,2,3]]).replic(2,4) Connectivity([[0, 1, 2], [0, 2, 3], [4, 5, 6], [4, 6, 7]]) """ return Connectivity( np.concatenate([self+i*inc for i in range(n)]), eltype=self.eltype)
[docs] def chain(self, disconnect=None, return_conn=False): """Reorder the elements into simply connected chains. Chaining the elements involves reordering them such that the first node of the next element is equal to the last node of the previous. This is especially useful in converting line elements to continuous curves or polylines. It will work with any plexitude though, and only look at the first and last node of the elements in the chaining process. Parameters ---------- disconnect: int :term:`array_like` | str, optional List of node numbers where the resulting chains should be split. None of the resulting chains will have any of the listed node numbers as an interior node. A chain may start and end at such a node. A special value 'branch' will set the disconnect array to all the nodes owned by more than two elements. This will split all chains at branching points. return_conn: bool If True, also return the list of Connectivities corresponding with the chains. Returns ------- chains: list of int arrays A list of tables with the same column length as those in ``conn``, and having two columns. The first column contains the original element numbers of a chain, and the second column a value +1 or -1 depending on whether the element traversal in the connected segment is in the original direction (+1) or the reverse (-1). The list of chains is sorted in order of decreasing length. conn: list of :class:`Connectivity` instances, optional Only returned if ``return_conn`` is True: a list a Connectivity tables of plexitude ``nplex`` corresponding to each chain. The elements in each Connectivity are ordered to form a continuous connected segment, i.e. the last node of each element in the table is equal to the first node of the following element (if any). See Also -------- chained: return only the chained Connectivities Examples -------- >>> Connectivity([[0,1],[1,2],[0,4],[4,2]]).chain() [array([[ 0, 1], [ 1, 1], [ 3, -1], [ 2, -1]])] >>> Connectivity([[0,1],[1,2],[0,4]]).chain() [array([[ 1, -1], [ 0, -1], [ 2, 1]])] >>> Connectivity([[0,1],[0,2],[0,3],[5,4]]).chain() [array([[ 0, -1], [ 1, 1]]), array([[3, 1]]), array([[2, 1]])] >>> Connectivity([[0,1],[0,2],[0,3],[5,4]]).chain(disconnect='branch') [array([[3, 1]]), array([[2, 1]]), array([[1, 1]]), array([[0, 1]])] >>> Connectivity([[0,1],[0,2],[0,3],[5,4]]).chain(return_conn=True) ([array([[ 0, -1], [ 1, 1]]), array([[3, 1]]), array([[2, 1]])], [Connectivity([[1, 0], [0, 2]]), Connectivity([[5, 4]]), Connectivity([[0, 3]])]) >>> Connectivity([[0,1,2],[2,0,3],[0,3,1],[4,5,2]]).chain() [array([[ 1, -1], [ 0, -1], [ 2, 1]]), array([[3, 1]])] >>> Connectivity([[0,1,2],[2,0,3],[0,3,1],[4,5,2]]).chain( ... disconnect=[0]) [array([[0, 1], [1, 1]]), array([[3, 1]]), array([[2, 1]])] """ elems = self[:,[0, -1]] # this allows for plexitudes > 2 elnrs = np.arange(elems.shape[0]) # original element numbers if disconnect == 'branch': disconnect = np.where(elems.nParents() > 2)[0] # !! nParents computes and stores the inverse, which makes # elems readonly; so we make it writable again elems.inv = None elems.flags.writeable = True chains = [] ind = np.zeros((elems.shape[0], 2), dtype=at.Int) while elems.size != 0: ie = 0 je = 0 rev = False k = elems[0][0] # remember startpoint while True: # Store an element that has been found ok if rev: ind[ie] = (je, -1) j = elems[je, 0] else: ind[ie] = (je, +1) j = elems[je, 1] ie += 1 elems[je] = -1 # Done with this one if j == k or (disconnect is not None and j in disconnect): break # Look for the next connected element w = np.where(elems[:] == j) if w[0].size == 0: # We've reached the end of a branch if disconnect is not None and k in disconnect: # not allowed to revert and continue past start point break # Try reversing w = np.where(elems[:, [0, -1]] == k) if w[0].size == 0: break else: j, k = k, j # reverse the table (colums and rows) ind[:ie] = ind[ie-1::-1].copy() # rows only ind[:ie, 1] *= -1 # change sign of 2nd column je = w[0][0] rev = w[-1][0] > 0 # check if the target node is the first or last indi = ind[:ie] # get the relevant part indi[:,0] = elnrs[indi[:, 0]] # translate element numbers chains.append(indi.copy()) todo = (elems!=-1).any(axis=1) elems = elems[todo] elnrs = elnrs[todo] # sort according to decreasing number of elements nel = [len(c) for c in chains] srt = np.argsort(nel)[::-1] chains = [chains[i] for i in srt] if not return_conn: return chains conn = [] for i,c in enumerate(chains): if c[:,1].sum() < 0: c[:,1] = - c[:,1] chains[i] = c = c[::-1] e = c[:,0] d = c[:,1] == -1 els = self[e] els[d] = els[d,::-1] conn.append(els) return chains,conn
[docs] def chained(self, disconnect=None): """Return the Connectivities of the chained elements. This is a convenience method calling :meth:`chain` with the ``return_conn=True`` parameter and only returning the second return value. It is equivalent with:: self.chain(disconnect, return_conn=True)[1] Examples -------- >>> Connectivity([[0,1],[1,2],[0,4],[4,2]]).chained() [Connectivity([[0, 1], [1, 2], [2, 4], [4, 0]])] >>> Connectivity([[0,1],[1,2],[0,4]]).chained() [Connectivity([[4, 0], [0, 1], [1, 2]])] >>> Connectivity([[0,1],[0,2],[0,3],[4,5]]).chained() [Connectivity([[1, 0], [0, 2]]), Connectivity([[4, 5]]), Connectivity([[0, 3]])] >>> Connectivity([[0,1],[0,2],[0,3],[5,4]]).chained(disconnect='branch') [Connectivity([[5, 4]]), Connectivity([[0, 3]]), Connectivity([[0, 2]]), Connectivity([[0, 1]])] >>> Connectivity([[0,1,2],[2,0,3],[0,3,1],[4,5,2]]).chained() [Connectivity([[1, 3, 0], [0, 1, 2], [2, 0, 3]]), Connectivity([[4, 5, 2]])] >>> Connectivity([[0,1,2],[2,0,3],[0,3,1],[4,5,2]],).chained( ... disconnect=[0]) [Connectivity([[0, 1, 2], [2, 0, 3]]), \ Connectivity([[4, 5, 2]]), Connectivity([[0, 3, 1]])] """ return self.chain(disconnect, return_conn=True)[1]
################################################################# # class and static methods #
[docs] @staticmethod def connect(clist, nodid=None, bias=None, loop=False): """Connect nodes from multiple Connectivity objects. Parameters ---------- clist: list of Connectivity objects The Connectivities to connect. nodid: int :term:`array_like`, optional List of node indices, same length as ``clist``. This specifies which node of the elements will be used in the connect operation. bias: int :term:`array_like`, optional List of element bias values, same length as ``clist``. If provided, then element looping will start at this number instead of at zero. loop: bool If False (default), new element generation will stop as soon as the shortest Connectivity runs out of elements. If set to True, the shorter lists will wrap around until all elements of all Connectivities have been used. Returns ------- Connectivity A Connectivity with plexitude equal to the number of Connectivities in ``clist``. Each element of the new Connectivity consist of a node from the corresponding element of each of the Connectivities in ``clist``. By default this will be the first node of that element, but a ``nodid`` list may be given to specify the node index to be used for each of the Connectivities. Finally, a list of bias values may be given to specify an offset in element number for the subsequent Connectivities. If loop==False, the length of the Connectivity will be the minimum length of the Connectivities in ``clist``, each minus its respective bias. If loop=True, the length will be the maximum length in of the Connectivities in ``clist``. Examples -------- >>> a = Connectivity([[0,1],[2,3],[4,5]]) >>> b = Connectivity([[10,11,12],[13,14,15]]) >>> c = Connectivity([[20,21],[22,23]]) >>> print(Connectivity.connect([a,b,c])) [[ 0 10 20] [ 2 13 22]] >>> print(Connectivity.connect([a,b,c],nodid=[1,0,1])) [[ 1 10 21] [ 3 13 23]] >>> print(Connectivity.connect([a,b,c],bias=[1,0,1])) [[ 2 10 22]] >>> print(Connectivity.connect([a,b,c],bias=[1,0,1],loop=True)) [[ 2 10 22] [ 4 13 20] [ 0 10 22]] """ try: m = len(clist) for i in range(m): if isinstance(clist[i], Connectivity): pass elif isinstance(clist[i], np.ndarray): clist[i] = Connectivity(clist[i]) else: raise TypeError except TypeError: raise TypeError('Connectivity.connect(): first argument should be a list of Connectivities') if not nodid: nodid = [0 for i in range(m)] if not bias: bias = [0 for i in range(m)] if loop: n = max([clist[i].nelems() for i in range(m)]) else: n = min([clist[i].nelems() - bias[i] for i in range(m)]) f = np.zeros((n, m), dtype=at.Int) for i, j, k in zip(range(m), nodid, bias): v = clist[i][k:k+n, j] if loop and k > 0: v = np.concatenate([v, clist[i][:k, j]]) f[:, i] = np.resize(v, (n)) return Connectivity(f)
############################################################################ # Private functions for adjacency multiprocessing def _elem_adj(inv, els, check): """Return elem adj for (part of) the elements""" adj = inv[els].reshape((els.shape[0], -1)) return Adjacency(adj, check_max=check) def _elem_adj_multi(inv, els, nproc=-1): from pyformex import multi datablocks = at.splitar(els, nproc) datalen = [0] + [d.shape[0] for d in datablocks] shift = np.array(datalen[:-1]).cumsum() tasks = [(_elem_adj, (inv, e, False)) for e, s in zip(datablocks, shift)] return multi.multitask(tasks, nproc=nproc) ###################################### # Deprecated @utils.deprecated_by("connectivity.connectedLineElems","Connectivity.chained") def connectedLineElems(elems, *args,**kargs): return elems.chained() # End