"""
Various graph related utilities.
"""
import networkx as nx
from openmdao.utils.general_utils import all_ancestors, common_subpath
from openmdao.utils.units import _find_unit
[docs]def get_sccs_topo(graph):
"""
Return strongly connected subsystems of the given Group in topological order.
Parameters
----------
graph : networkx.DiGraph
Directed graph of Systems.
Returns
-------
list of sets of str
A list of strongly connected components in topological order.
"""
# Tarjan's algorithm returns SCCs in reverse topological order, so
# the list returned here is reversed.
sccs = list(nx.strongly_connected_components(graph))
sccs.reverse()
return sccs
[docs]def get_out_of_order_nodes(graph, orders):
"""
Return a list of nodes that are out of order.
Parameters
----------
graph : networkx.DiGraph
Directed graph of Systems.
orders : dict
A dict of order values keyed by node name.
Returns
-------
list of sets of str
A list of strongly connected components in topological order.
list of str
A list of nodes that are out of order.
"""
strongcomps = get_sccs_topo(graph)
out_of_order = []
for strongcomp in strongcomps:
for u, v in graph.edges(strongcomp):
# for any connection between a system in this strongcomp and a system
# outside of it, the target must be ordered after the source.
if u in strongcomp and v not in strongcomp and orders[u] > orders[v]:
out_of_order.append((u, v))
return strongcomps, out_of_order
[docs]def get_cycle_tree(group):
"""
Compute the tree of cycles for the given group.
Parameters
----------
group : <Group>
The specified Group.
Returns
-------
networkx.DiGraph
The component graph for the given Group.
dict
A mapping of group path name to a tuple of the form
(children, recursive_scc, unique_scc, scc_index, path, parent path or None).
"""
from openmdao.core.group import iter_solver_info, Group
G = group.compute_sys_graph(comps_only=True, add_edge_info=False)
topo = get_sccs_topo(G)
topsccs = [s for s in topo if len(s) > 1]
common_paths = [common_subpath(s) for s in topsccs]
cpathdict = {}
for cpath, s in zip(common_paths, topsccs):
if cpath not in cpathdict:
cpathdict[cpath] = []
cpathdict[cpath].append(s)
topname = group.pathname
group_tree_dict = {}
for cpath, cpsccs in cpathdict.items():
group_tree_dict[cpath] = [([], scc, set(scc), i, cpath, None)
for i, scc in enumerate(cpsccs)]
it = group._sys_tree_visitor(iter_solver_info, predicate=lambda s: isinstance(s, Group),
yield_none=False)
for tup in sorted(it, key=lambda x: (x[0].count('.'), len(x[0]))):
path = tup[0]
if not tup[2]: # no sccs
continue
for ans in all_ancestors(path):
if ans in group_tree_dict:
parent_tree = group_tree_dict[ans]
break
else:
parent_tree = group_tree_dict[topname]
tree = group_tree_dict[path] if path in group_tree_dict else None
prefix = path + '.' if path else ''
for children, parent_scc, unique, _, parpath, _ in parent_tree:
if prefix:
matching_comps = [c for c in parent_scc if c.startswith(prefix)]
else:
matching_comps = parent_scc
if matching_comps:
subgraph = G.subgraph(matching_comps)
sub_sccs = [s for s in get_sccs_topo(subgraph) if len(s) > 1]
for sub_scc in sub_sccs:
if not sub_scc.isdisjoint(parent_scc) and sub_scc != parent_scc:
if tree is None:
group_tree_dict[path] = tree = ([])
tree.append(([], sub_scc, set(sub_scc), len(tree), path, parpath))
children.append(tree[-1])
# remmove the childs scc comps from the parent 'unique' scc
unique.difference_update(sub_scc)
return G, group_tree_dict
[docs]def print_cycle_tree(group):
"""
Print the tree of cycles for the given group.
Parameters
----------
group : <Group>
The specified Group.
"""
G, group_tree_dict = get_cycle_tree(group)
def _print_tree(node, nscc, indent=''):
children, scc, unique, i, path, _ = node
print(indent, f"cycle {i + 1} of {nscc} for '{path}'")
for u in unique:
print(indent, f" {u}")
if children:
for tup in children:
_print_tree(tup, len(group_tree_dict[tup[4]]), indent + ' ')
for lst in group_tree_dict.values():
for _, _, _, idx, _, parpath in lst:
if parpath is None: # this is a top level scc
_print_tree(lst[idx], len(lst))
[docs]def get_unresolved_knowns(graph, meta_name, nodes):
"""
Return all unresolved nodes with known shape.
Unresolved means that the node has known shape and at least one neighbor
with unknown shape.
Parameters
----------
graph : nx.DiGraph
Graph containing all variables with shape info.
meta_name : str
The name of the node metadata variable to check.
nodes : set of str
Set of nodes to check. All nodes must be in the graph.
Returns
-------
set of str
Set of nodes with known shape but at least one neighbor with unknown shape.
"""
gnodes = graph.nodes
unresolved = set()
for node in nodes:
if gnodes[node][meta_name] is not None: # node has known shape
for succ in graph.successors(node):
if gnodes[succ][meta_name] is None:
unresolved.add(node)
break
for pred in graph.predecessors(node):
if gnodes[pred][meta_name] is None:
unresolved.add(node)
break
return unresolved
[docs]def is_unresolved(graph, node, meta_name):
"""
Return True if the given node is unresolved.
Unresolved means that the node has at least one neighbor with unknown shape.
Parameters
----------
graph : nx.DiGraph
Graph containing all variables with shape info.
node : str
Node to check.
meta_name : str
The name of the node metadata variable to check.
Returns
-------
bool
True if the node is unresolved.
"""
nodes = graph.nodes
for s in graph.successors(node):
if nodes[s][meta_name] is None:
return True
for p in graph.predecessors(node):
if nodes[p][meta_name] is None:
return True
return False
[docs]def are_connected(graph, start, end):
"""
Return True if the given source and target are connected.
Parameters
----------
graph : networkx.DiGraph
Directed graph of Systems and variables.
start : str
Name of the starting node.
end : str
Name of the ending node.
Returns
-------
bool
True if the given source and target are connected.
"""
if start in graph and end in graph:
successors = graph.successors
stack = [start]
visited = set(stack)
while stack:
start = stack.pop()
for node in successors(start):
if node == end:
return True
if node not in visited:
visited.add(node)
stack.append(node)
return False
[docs]def get_active_edges(graph, knowns, meta_name):
"""
Return all active single edges and active multi nodes.
Active edges are those that are connected on one end to a variable with 'known' metadata
and on the other end to a variable with 'unknown' metadata. Active nodes are those that
have 'unknown' metadata but are connected to a variable with 'known' metadata.
Single edges correspond to 'x_by_conn' and 'copy_x' connections.
Multi nodes are variables that have 'compute_x' set to True so they
connect to multiple nodes of the opposite io type in a component. For example
a 'compute_shape' output variable will connect to all inputs in the component and
each of those edges will be labeled as 'multi'. So a multi node is a node that
has 'multi' incoming edges.
Parameters
----------
graph : nx.DiGraph
Graph containing all variables with known/unknown info.
knowns : list of str
List of nodes with 'known' metadata.
meta_name : str
The name of the node metadata to check for 'known'/'unknown' status.
Returns
-------
active_single_edges : set of (str, str)
Set of active 'single' edges (for copy_x and x_by_conn).
computed_nodes : set of str
Set of active nodes with 'multi' edges (for compute_x).
"""
nodes = graph.nodes
edges = graph.edges
active_single_edges = set()
computed_nodes = set()
for known in knowns:
for succ in graph.successors(known):
if nodes[succ][meta_name] is None:
if edges[known, succ]['multi']:
computed_nodes.add(succ)
else:
active_single_edges.add((known, succ))
# We don't need to loop over predecessors here because this graph is not a dataflow
# graph where data always flows from outputs to inputs. In this case, the direction of
# each edge is determined by the presence of shape_by_conn, etc., so for example, if an
# output has shape_by_conn, then this graph has an edge from the connected input to
# that output, which is the opposite direction of the edge between the same two variables
# in our typical dataflow graph. Since in this function we always start at 'known'
# nodes, we only need to check their successors.
return active_single_edges, computed_nodes
_shape_extract = ('distributed', 'shape', 'compute_shape', 'shape_by_conn', 'copy_shape')
_units_extract = ('units', 'compute_units', 'units_by_conn', 'copy_units')
[docs]def add_shape_node(graph, name, io, meta):
"""
Add a shape node to the graph.
Parameters
----------
graph : networkx.DiGraph
Graph to add the shape node to.
name : str
Name of the shape node.
io : str
Input or output.
meta : dict
Metadata for the variable.
"""
kwargs = {k: meta[k] for k in _shape_extract}
if io == 'input':
kwargs['src_indices'] = meta.get('src_indices')
kwargs['flat_src_indices'] = meta.get('flat_src_indices')
graph.add_node(name, io=io, **kwargs)
[docs]def add_units_node(graph, name, io, meta):
"""
Add a units node to the graph.
Parameters
----------
graph : networkx.DiGraph
Graph to add the units node to.
name : str
Name of the units node.
io : str
Input or output.
meta : dict
Metadata for the variable.
"""
kwargs = {k: meta[k] for k in _units_extract}
if kwargs['units'] is not None:
# Turn units data into a PhysicalUnit so units of expressions can be computed.
kwargs['units'] = _find_unit(kwargs['units'])
graph.add_node(name, io=io, **kwargs)
