/** Get a graph and direct only the unshielded colliders. */
public static void basicPattern(Graph graph) {
Set<Edge> undirectedEdges = new HashSet<Edge>();
NEXT_EDGE:
for (Edge edge : graph.getEdges()) {
Node head = null, tail = null;
if (edge.getEndpoint1() == Endpoint.ARROW && edge.getEndpoint2() == Endpoint.TAIL) {
head = edge.getNode1();
tail = edge.getNode2();
} else if (edge.getEndpoint2() == Endpoint.ARROW && edge.getEndpoint1() == Endpoint.TAIL) {
head = edge.getNode2();
tail = edge.getNode1();
}
if (head != null) {
for (Node node : graph.getParents(head)) {
if (node != tail && !graph.isAdjacentTo(tail, node)) {
continue NEXT_EDGE;
}
}
undirectedEdges.add(edge);
}
}
for (Edge nextUndirected : undirectedEdges) {
Node node1 = nextUndirected.getNode1(), node2 = nextUndirected.getNode2();
graph.removeEdge(nextUndirected);
graph.addUndirectedEdge(node1, node2);
}
}
public Graph orient() {
Graph skeleton = GraphUtils.undirectedGraph(getPattern());
Graph graph = new EdgeListGraph(skeleton.getNodes());
List<Node> nodes = skeleton.getNodes();
// Collections.shuffle(nodes);
if (isR1Done()) {
ruleR1(skeleton, graph, nodes);
}
for (Edge edge : skeleton.getEdges()) {
if (!graph.isAdjacentTo(edge.getNode1(), edge.getNode2())) {
graph.addUndirectedEdge(edge.getNode1(), edge.getNode2());
}
}
if (isR2Done()) {
ruleR2(skeleton, graph);
}
if (isMeekDone()) {
new MeekRules().orientImplied(graph);
}
return graph;
}
/**
* Transforms a maximally directed pattern (PDAG) represented in graph <code>g</code> into an
* arbitrary DAG by modifying <code>g</code> itself. Based on the algorithm described in
* Chickering (2002) "Optimal structure identification with greedy search" Journal of Machine
* Learning Research. R. Silva, June 2004
*/
public static void pdagToDag(Graph g) {
Graph p = new EdgeListGraph(g);
List<Edge> undirectedEdges = new ArrayList<Edge>();
for (Edge edge : g.getEdges()) {
if (edge.getEndpoint1() == Endpoint.TAIL
&& edge.getEndpoint2() == Endpoint.TAIL
&& !undirectedEdges.contains(edge)) {
undirectedEdges.add(edge);
}
}
g.removeEdges(undirectedEdges);
List<Node> pNodes = p.getNodes();
do {
Node x = null;
for (Node pNode : pNodes) {
x = pNode;
if (p.getChildren(x).size() > 0) {
continue;
}
Set<Node> neighbors = new HashSet<Node>();
for (Edge edge : p.getEdges()) {
if (edge.getNode1() == x || edge.getNode2() == x) {
if (edge.getEndpoint1() == Endpoint.TAIL && edge.getEndpoint2() == Endpoint.TAIL) {
if (edge.getNode1() == x) {
neighbors.add(edge.getNode2());
} else {
neighbors.add(edge.getNode1());
}
}
}
}
if (neighbors.size() > 0) {
Collection<Node> parents = p.getParents(x);
Set<Node> all = new HashSet<Node>(neighbors);
all.addAll(parents);
if (!GraphUtils.isClique(all, p)) {
continue;
}
}
for (Node neighbor : neighbors) {
Node node1 = g.getNode(neighbor.getName());
Node node2 = g.getNode(x.getName());
g.addDirectedEdge(node1, node2);
}
p.removeNode(x);
break;
}
pNodes.remove(x);
} while (pNodes.size() > 0);
}
public void setParameterValue(Edge edge, double value) {
if (Edges.isDirectedEdge(edge)) {
setEdgeCoefficient(edge.getNode1(), edge.getNode2(), value);
} else if (Edges.isBidirectedEdge(edge)) {
setErrorCovariance(edge.getNode1(), edge.getNode2(), value);
} else {
throw new IllegalArgumentException(
"Only directed and bidirected edges are supported: " + edge);
}
}
public TimeLagGraphWrapper(GraphWrapper graphWrapper) {
if (graphWrapper == null) {
throw new NullPointerException("No graph wrapper.");
}
TimeLagGraph graph = new TimeLagGraph();
Graph _graph = graphWrapper.getGraph();
for (Node node : _graph.getNodes()) {
Node _node = node.like(node.getName() + ":0");
_node.setNodeType(node.getNodeType());
graph.addNode(_node);
}
for (Edge edge : _graph.getEdges()) {
if (!Edges.isDirectedEdge(edge)) {
throw new IllegalArgumentException();
}
Node from = edge.getNode1();
Node to = edge.getNode2();
Node _from = graph.getNode(from.getName(), 1);
Node _to = graph.getNode(to.getName(), 0);
graph.addDirectedEdge(_from, _to);
}
this.graph = graph;
}
private Graph condense(Graph mimStructure, Graph mimbuildStructure) {
// System.out.println("Uncondensed: " + mimbuildStructure);
Map<Node, Node> substitutions = new HashMap<Node, Node>();
for (Node node : mimbuildStructure.getNodes()) {
for (Node _node : mimStructure.getNodes()) {
if (node.getName().startsWith(_node.getName())) {
substitutions.put(node, _node);
break;
}
substitutions.put(node, node);
}
}
HashSet<Node> nodes = new HashSet<Node>(substitutions.values());
Graph graph = new EdgeListGraph(new ArrayList<Node>(nodes));
for (Edge edge : mimbuildStructure.getEdges()) {
Node node1 = substitutions.get(edge.getNode1());
Node node2 = substitutions.get(edge.getNode2());
if (node1 == node2) continue;
if (graph.isAdjacentTo(node1, node2)) continue;
graph.addEdge(new Edge(node1, node2, edge.getEndpoint1(), edge.getEndpoint2()));
}
// System.out.println("Condensed: " + graph);
return graph;
}
/**
* This helper calculates all the attractive forces onto a node. Attractive forces from from the
* edges pulling nodes towards each other, this will love through the edges of this node.
*
* @param current Node to calculate forces for.
*/
private void calculateNodeAttractiveForce(Node current) {
// get all the edges of the current node
ArrayList<Edge> nodeEdgeList = current.getEdgeList();
// of each of this node's edge do attactive forces
Iterator<Edge> nodeEdges = nodeEdgeList.iterator();
///
int numOfEdgesWeight = 10 * (int) Math.round(nodeEdgeList.size() + SPACING);
// Loop through edges and find edges containing current node
while (nodeEdges.hasNext()) {
Edge e = nodeEdges.next();
double edgeStrength = e.getStrength();
Node n;
int dx, dy;
double sign = 1.0;
if (current == e.getNode1()) {
n = e.getNode2();
dx = current.getX() - n.getX();
dy = current.getY() - n.getY();
} else {
n = e.getNode1();
dx = current.getX() - n.getX();
dy = current.getY() - n.getY();
sign = -1.0;
}
double distance = Math.sqrt(dx * dx + dy * dy) + .1;
// multiply by the strength of edge
// current.setVX(current.getVX() - dx / numOfEdgesWeight * edgeStrength);
// current.setVY(current.getVY() - dy / numOfEdgesWeight * edgeStrength);
current.accelx += sign * (dx * STIFFNESS * (SPRING_LENGTH - distance)) / current.weight;
current.accely += sign * (dy * STIFFNESS * (SPRING_LENGTH - distance)) / current.weight;
// current.accelx += sign * (dx * (e.getStrength() + 1) * (SPRING_LENGTH - distance) * 0.5) /
// current.weight;
// current.accely += sign * (dy * (e.getStrength() + 1) * (SPRING_LENGTH - distance) * 0.5) /
// current.weight;
// n.accelx += sign * (dx * (e.getStrength() + 1) * (SPRING_LENGTH - distance) * 0.5) /
// n.weight;
// n.accely += sign * (dy * (e.getStrength() + 1) * (SPRING_LENGTH - distance) * 0.5) /
// n.weight;
}
}
public boolean containsParameter(Edge edge) {
if (Edges.isBidirectedEdge(edge)) {
edge =
Edges.bidirectedEdge(
semGraph.getExogenous(edge.getNode1()), semGraph.getExogenous(edge.getNode2()));
}
return edgeParameters.keySet().contains(edge);
}
private void calcStats() {
// Graph resultGraph = getAlgorithmRunner().getResultGraph();
IGesRunner runner = (IGesRunner) getAlgorithmRunner();
if (runner.getTopGraphs().isEmpty()) {
throw new IllegalArgumentException(
"No patterns were recorded. Please adjust the number of " + "patterns to store.");
}
Graph resultGraph = runner.getTopGraphs().get(runner.getIndex()).getGraph();
if (getAlgorithmRunner().getDataModel() instanceof DataSet) {
// resultGraph may be the output of a PC search.
// Such graphs sometimes contain doubly directed edges.
// /We converte such edges to directed edges here.
// For the time being an orientation is arbitrarily selected.
Set<Edge> allEdges = resultGraph.getEdges();
for (Edge edge : allEdges) {
if (edge.getEndpoint1() == Endpoint.ARROW && edge.getEndpoint2() == Endpoint.ARROW) {
// Option 1 orient it from node1 to node2
resultGraph.setEndpoint(edge.getNode1(), edge.getNode2(), Endpoint.ARROW);
// Option 2 remove such edges:
resultGraph.removeEdge(edge);
}
}
Pattern pattern = new Pattern(resultGraph);
PatternToDag ptd = new PatternToDag(pattern);
Graph dag = ptd.patternToDagMeekRules();
DataSet dataSet = (DataSet) getAlgorithmRunner().getDataModel();
String report;
if (dataSet.isContinuous()) {
report = reportIfContinuous(dag, dataSet);
} else if (dataSet.isDiscrete()) {
report = reportIfDiscrete(dag, dataSet);
} else {
throw new IllegalArgumentException("");
}
JScrollPane dagWorkbenchScroll = dagWorkbenchScroll(dag);
modelStatsText.setLineWrap(true);
modelStatsText.setWrapStyleWord(true);
modelStatsText.setText(report);
removeStatsTabs();
tabbedPane.addTab("DAG in pattern", dagWorkbenchScroll);
tabbedPane.addTab("DAG Model Statistics", modelStatsText);
}
}
/**
* Forward equivalence search.
*
* @param graph The graph in the state prior to the forward equivalence search.
*/
private void fes(Graph graph, List<Node> nodes) {
TetradLogger.getInstance().log("info", "** FORWARD EQUIVALENCE SEARCH");
lookupArrows = new HashMap<OrderedPair, Set<Arrow>>();
initializeArrowsForward(nodes);
while (!sortedArrows.isEmpty()) {
Arrow arrow = sortedArrows.first();
sortedArrows.remove(arrow);
Node x = arrow.getX();
Node y = arrow.getY();
clearArrow(x, y);
if (graph.isAdjacentTo(x, y)) {
continue;
}
if (!validInsert(x, y, arrow.getHOrT(), arrow.getNaYX(), graph)) {
continue;
}
List<Node> t = arrow.getHOrT();
double bump = arrow.getBump();
Set<Edge> edges = graph.getEdges();
insert(x, y, t, graph, bump);
score += bump;
rebuildPattern(graph);
// Try to avoid duplicating scoring calls. First clear out all of the edges that need to be
// changed,
// then change them, checking to see if they're already been changed. I know, roundabout, but
// there's
// a performance boost.
for (Edge edge : graph.getEdges()) {
if (!edges.contains(edge)) {
reevaluateForward(graph, nodes, edge.getNode1(), edge.getNode2());
}
}
storeGraph(graph);
}
}
public void deleteElement(MapElement m) {
if (m instanceof Node) {
Node n = (Node) m;
Vector<Node> nodes = getNodes();
nodes.remove(m);
Vector<Edge> edgesLeft = new Vector<Edge>();
for (int i = 0; i < edges.size(); i++) {
Edge e = edges.get(i);
if (e.getNode1() != n && e.getNode2() != n) {
edgesLeft.add(e);
}
}
edges = edgesLeft;
} else if (m instanceof Edge) {
edges.remove(m);
}
}
public static Graph weightedRandomGraph(int n, int e) {
List<Node> nodes = new ArrayList<Node>();
for (int i = 0; i < n; i++) nodes.add(new GraphNode("X" + i));
Graph graph = new EdgeListGraph(nodes);
for (int e0 = 0; e0 < e; e0++) {
int i1 = weightedRandom(nodes, graph);
// int i2 = RandomUtil.getInstance().nextInt(n);
int i2 = weightedRandom(nodes, graph);
if (!(shortestPath(nodes.get(i1), nodes.get(i2), graph) < 9)) {
e0--;
continue;
}
if (i1 == i2) {
e0--;
continue;
}
Edge edge = Edges.undirectedEdge(nodes.get(i1), nodes.get(i2));
if (graph.containsEdge(edge)) {
e0--;
continue;
}
graph.addEdge(edge);
}
for (Edge edge : graph.getEdges()) {
Node n1 = edge.getNode1();
Node n2 = edge.getNode2();
if (!graph.isAncestorOf(n2, n1)) {
graph.removeEdge(edge);
graph.addDirectedEdge(n1, n2);
} else {
graph.removeEdge(edge);
graph.addDirectedEdge(n2, n1);
}
}
return graph;
}
private void ruleR2(Graph skeleton, Graph graph) {
Set<Edge> edgeList1 = skeleton.getEdges();
// Collections.shuffle(edgeList1);
for (Edge adj : edgeList1) {
Node x = adj.getNode1();
Node y = adj.getNode2();
if (!isR2Orient2Cycles() && isTwoCycle(graph, x, y)) {
continue;
}
if (!isTwoCycle(graph, x, y) && !isUndirected(graph, x, y)) {
continue;
}
resolveOneEdgeMax(graph, x, y, isStrongR2(), new EdgeListGraph(graph));
}
}
private void initializeArrowsBackward(Graph graph) {
sortedArrows.clear();
lookupArrows.clear();
for (Edge edge : graph.getEdges()) {
Node x = edge.getNode1();
Node y = edge.getNode2();
if (!knowledgeEmpty()) {
if (!getKnowledge().noEdgeRequired(x.getName(), y.getName())) {
continue;
}
}
if (Edges.isDirectedEdge(edge)) {
calculateArrowsBackward(x, y, graph);
} else {
calculateArrowsBackward(x, y, graph);
calculateArrowsBackward(y, x, graph);
}
}
}
private Graph pickDag(Graph graph) {
SearchGraphUtils.basicPattern(graph, false);
addRequiredEdges(graph);
boolean containsUndirected;
do {
containsUndirected = false;
for (Edge edge : graph.getEdges()) {
if (Edges.isUndirectedEdge(edge)) {
containsUndirected = true;
graph.removeEdge(edge);
Edge _edge = Edges.directedEdge(edge.getNode1(), edge.getNode2());
graph.addEdge(_edge);
}
}
meekOrient(graph, getKnowledge());
} while (containsUndirected);
return graph;
}
/**
* @return The edge coefficient matrix of the model, a la SemIm. Note that this will normally need
* to be transposed, since [a][b] is the edge coefficient for a-->b, not b-->a. Sorry.
* History. THESE ARE PARAMETERS OF THE MODEL--THE ONLY PARAMETERS.
*/
public TetradMatrix edgeCoef() {
List<Node> variableNodes = getVariableNodes();
TetradMatrix edgeCoef = new TetradMatrix(variableNodes.size(), variableNodes.size());
for (Edge edge : edgeParameters.keySet()) {
if (Edges.isBidirectedEdge(edge)) {
continue;
}
Node a = edge.getNode1();
Node b = edge.getNode2();
int aindex = variableNodes.indexOf(a);
int bindex = variableNodes.indexOf(b);
double coef = edgeParameters.get(edge);
edgeCoef.set(aindex, bindex, coef);
}
return edgeCoef;
}
/**
* Transforms a DAG represented in graph <code>graph</code> into a maximally directed pattern
* (PDAG) by modifying <code>g</code> itself. Based on the algorithm described in Chickering
* (2002) "Optimal structure identification with greedy search" Journal of Machine Learning
* Research. It works for both BayesNets and SEMs. R. Silva, June 2004
*/
public static void dagToPdag(Graph graph) {
// do topological sort on the nodes
Graph graphCopy = new EdgeListGraph(graph);
Node orderedNodes[] = new Node[graphCopy.getNodes().size()];
int count = 0;
while (graphCopy.getNodes().size() > 0) {
Set<Node> exogenousNodes = new HashSet<Node>();
for (Node next : graphCopy.getNodes()) {
if (graphCopy.isExogenous(next)) {
exogenousNodes.add(next);
orderedNodes[count++] = graph.getNode(next.getName());
}
}
graphCopy.removeNodes(new ArrayList<Node>(exogenousNodes));
}
// ordered edges - improvised, inefficient implementation
count = 0;
Edge edges[] = new Edge[graph.getNumEdges()];
boolean edgeOrdered[] = new boolean[graph.getNumEdges()];
Edge orderedEdges[] = new Edge[graph.getNumEdges()];
for (Edge edge : graph.getEdges()) {
edges[count++] = edge;
}
for (int i = 0; i < edges.length; i++) {
edgeOrdered[i] = false;
}
while (count > 0) {
for (Node orderedNode : orderedNodes) {
for (int k = orderedNodes.length - 1; k >= 0; k--) {
for (int q = 0; q < edges.length; q++) {
if (!edgeOrdered[q]
&& edges[q].getNode1() == orderedNodes[k]
&& edges[q].getNode2() == orderedNode) {
edgeOrdered[q] = true;
orderedEdges[orderedEdges.length - count] = edges[q];
count--;
}
}
}
}
}
// label edges
boolean compelledEdges[] = new boolean[graph.getNumEdges()];
boolean reversibleEdges[] = new boolean[graph.getNumEdges()];
for (int i = 0; i < graph.getNumEdges(); i++) {
compelledEdges[i] = false;
reversibleEdges[i] = false;
}
for (int i = 0; i < graph.getNumEdges(); i++) {
if (compelledEdges[i] || reversibleEdges[i]) {
continue;
}
Node x = orderedEdges[i].getNode1();
Node y = orderedEdges[i].getNode2();
for (int j = 0; j < orderedEdges.length; j++) {
if (orderedEdges[j].getNode2() == x && compelledEdges[j]) {
Node w = orderedEdges[j].getNode1();
if (!graph.isParentOf(w, y)) {
for (int k = 0; k < orderedEdges.length; k++) {
if (orderedEdges[k].getNode2() == y) {
compelledEdges[k] = true;
break;
}
}
} else {
for (int k = 0; k < orderedEdges.length; k++) {
if (orderedEdges[k].getNode1() == w && orderedEdges[k].getNode2() == y) {
compelledEdges[k] = true;
break;
}
}
}
}
if (compelledEdges[i]) {
break;
}
}
if (compelledEdges[i]) {
continue;
}
boolean foundZ = false;
for (Edge orderedEdge : orderedEdges) {
Node z = orderedEdge.getNode1();
if (z != x && orderedEdge.getNode2() == y && !graph.isParentOf(z, x)) {
compelledEdges[i] = true;
for (int k = i + 1; k < graph.getNumEdges(); k++) {
if (orderedEdges[k].getNode2() == y && !reversibleEdges[k]) {
compelledEdges[k] = true;
}
}
foundZ = true;
break;
}
}
if (!foundZ) {
reversibleEdges[i] = true;
for (int j = i + 1; j < orderedEdges.length; j++) {
if (!compelledEdges[j] && orderedEdges[j].getNode2() == y) {
reversibleEdges[j] = true;
}
}
}
}
// undirect edges that are reversible
for (int i = 0; i < reversibleEdges.length; i++) {
if (reversibleEdges[i]) {
graph.setEndpoint(orderedEdges[i].getNode1(), orderedEdges[i].getNode2(), Endpoint.TAIL);
graph.setEndpoint(orderedEdges[i].getNode2(), orderedEdges[i].getNode1(), Endpoint.TAIL);
}
}
}
private void addRequiredEdges(Graph graph) {
if (true) return;
if (knowledgeEmpty()) return;
for (Iterator<KnowledgeEdge> it = getKnowledge().requiredEdgesIterator(); it.hasNext(); ) {
KnowledgeEdge next = it.next();
Node nodeA = graph.getNode(next.getFrom());
Node nodeB = graph.getNode(next.getTo());
if (!graph.isAncestorOf(nodeB, nodeA)) {
graph.removeEdges(nodeA, nodeB);
graph.addDirectedEdge(nodeA, nodeB);
TetradLogger.getInstance()
.log("insertedEdges", "Adding edge by knowledge: " + graph.getEdge(nodeA, nodeB));
}
}
for (Edge edge : graph.getEdges()) {
final String A = edge.getNode1().getName();
final String B = edge.getNode2().getName();
if (knowledge.isForbidden(A, B)) {
Node nodeA = edge.getNode1();
Node nodeB = edge.getNode2();
if (nodeA != null
&& nodeB != null
&& graph.isAdjacentTo(nodeA, nodeB)
&& !graph.isChildOf(nodeA, nodeB)) {
if (!graph.isAncestorOf(nodeA, nodeB)) {
graph.removeEdges(nodeA, nodeB);
graph.addDirectedEdge(nodeB, nodeA);
TetradLogger.getInstance()
.log("insertedEdges", "Adding edge by knowledge: " + graph.getEdge(nodeB, nodeA));
}
}
if (!graph.isChildOf(nodeA, nodeB)
&& getKnowledge().isForbidden(nodeA.getName(), nodeB.getName())) {
if (!graph.isAncestorOf(nodeA, nodeB)) {
graph.removeEdges(nodeA, nodeB);
graph.addDirectedEdge(nodeB, nodeA);
TetradLogger.getInstance()
.log("insertedEdges", "Adding edge by knowledge: " + graph.getEdge(nodeB, nodeA));
}
}
} else if (knowledge.isForbidden(B, A)) {
Node nodeA = edge.getNode2();
Node nodeB = edge.getNode1();
if (nodeA != null
&& nodeB != null
&& graph.isAdjacentTo(nodeA, nodeB)
&& !graph.isChildOf(nodeA, nodeB)) {
if (!graph.isAncestorOf(nodeA, nodeB)) {
graph.removeEdges(nodeA, nodeB);
graph.addDirectedEdge(nodeB, nodeA);
TetradLogger.getInstance()
.log("insertedEdges", "Adding edge by knowledge: " + graph.getEdge(nodeB, nodeA));
}
}
if (!graph.isChildOf(nodeA, nodeB)
&& getKnowledge().isForbidden(nodeA.getName(), nodeB.getName())) {
if (!graph.isAncestorOf(nodeA, nodeB)) {
graph.removeEdges(nodeA, nodeB);
graph.addDirectedEdge(nodeB, nodeA);
TetradLogger.getInstance()
.log("insertedEdges", "Adding edge by knowledge: " + graph.getEdge(nodeB, nodeA));
}
}
}
}
}
/**
* @param edge a->b or a<->b.
* @return the range of the covariance parameter for a->b or a<->b.
*/
public ParameterRange getParameterRange(Edge edge) {
if (Edges.isBidirectedEdge(edge)) {
edge =
Edges.bidirectedEdge(
semGraph.getExogenous(edge.getNode1()), semGraph.getExogenous(edge.getNode2()));
}
if (!(edgeParameters.keySet().contains(edge))) {
throw new IllegalArgumentException("Not an edge in this model: " + edge);
}
double initial = edgeParameters.get(edge);
if (initial == Double.NEGATIVE_INFINITY) {
initial = Double.MIN_VALUE;
} else if (initial == Double.POSITIVE_INFINITY) {
initial = Double.MAX_VALUE;
}
double value = initial;
// look upward for a point that fails.
double high = value + 1;
while (paramInBounds(edge, high)) {
high = value + 2 * (high - value);
if (high == Double.POSITIVE_INFINITY) {
break;
}
}
// find the boundary using binary search.
double rangeHigh;
if (high == Double.POSITIVE_INFINITY) {
rangeHigh = high;
} else {
double low = value;
while (high - low > 1e-10) {
double midpoint = (high + low) / 2.0;
if (paramInBounds(edge, midpoint)) {
low = midpoint;
} else {
high = midpoint;
}
}
rangeHigh = (high + low) / 2.0;
}
// look downard for a point that fails.
double low = value - 1;
while (paramInBounds(edge, low)) {
low = value - 2 * (value - low);
if (low == Double.NEGATIVE_INFINITY) {
break;
}
}
double rangeLow;
if (low == Double.NEGATIVE_INFINITY) {
rangeLow = low;
} else {
// find the boundary using binary search.
high = value;
while (high - low > 1e-10) {
double midpoint = (high + low) / 2.0;
if (paramInBounds(edge, midpoint)) {
high = midpoint;
} else {
low = midpoint;
}
}
rangeLow = (high + low) / 2.0;
}
if (Edges.isDirectedEdge(edge)) {
edgeParameters.put(edge, initial);
} else if (Edges.isBidirectedEdge(edge)) {
edgeParameters.put(edge, initial);
}
return new ParameterRange(edge, value, rangeLow, rangeHigh);
}