diff toolboxes/FullBNT-1.0.7/graph/trees.txt @ 0:e9a9cd732c1e tip

first hg version after svn

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolboxes/FullBNT-1.0.7/graph/trees.txt	Tue Feb 10 15:05:51 2015 +0000
@@ -0,0 +1,168 @@
+
+% make undirected adjacency matrix of graph/tree
+% e.g.,
+%  1 
+% / \
+% 2  3
+T = zeros(3,3);
+T(1,2) = 1; T(2,1)=1;
+T(1,3)=1; T(3,1) = 1;
+
+root = 1;
+[T, preorder, postorder] =  mk_rooted_tree(T, root);
+
+% bottom up message passing leaves to root
+for n=postorder(:)'
+  for p	= parents(T, n)
+     % p is parent of n
+   end
+end
+
+% top down, root to leaves
+for n=preorder(:)'
+  for c= children(T,n)
+    % c is child of n
+  end
+end
+
+
+%%%%%%%%%%%%%
+
+function ps = parents(adj_mat, i)
+% PARENTS Return the list of parents of node i
+% ps = parents(adj_mat, i)
+
+ps = find(adj_mat(:,i))';
+
+
+%%%%%%%%%%%%
+
+function cs = children(adj_mat, i, t)
+% CHILDREN Return the indices of a node's children in sorted order
+% c = children(adj_mat, i, t)
+%
+% t is an optional argument: if present, dag is assumed to be a 2-slice DBN
+
+if nargin < 3 
+  cs = find(adj_mat(i,:));
+else
+  if t==1
+    cs = find(adj_mat(i,:));
+  else
+    ss = length(adj_mat)/2;
+    j = i+ss;
+    cs = find(adj_mat(j,:)) + (t-2)*ss;
+  end
+end
+
+%%%%%%%%%%%
+
+function [T, pre, post, cycle] = mk_rooted_tree(G, root)
+% MK_ROOTED_TREE Make a directed, rooted tree out of an undirected tree.
+% [T, pre, post, cycle] = mk_rooted_tree(G, root)
+
+n = length(G);
+T = sparse(n,n); % not the same as T = sparse(n) !
+directed = 0;
+[d, pre, post, cycle, f, pred] = dfs(G, root, directed);
+for i=1:length(pred)
+  if pred(i)>0
+    T(pred(i),i)=1;
+  end
+end
+
+
+%%%%%%%%%%%
+
+function [d, pre, post, cycle, f, pred] = dfs(adj_mat, start, directed)
+% DFS Perform a depth-first search of the graph starting from 'start'.
+% [d, pre, post, cycle, f, pred] = dfs(adj_mat, start, directed)
+%
+% Input:
+% adj_mat(i,j)=1 iff i is connected to j.
+% start is the root vertex of the dfs tree; if [], all nodes are searched
+% directed = 1 if the graph is directed
+%
+% Output:
+% d(i) is the time at which node i is first discovered.
+% pre is a list of the nodes in the order in which they are first encountered (opened).
+% post is a list of the nodes in the order in which they are last encountered (closed).
+% 'cycle' is true iff a (directed) cycle is found.
+% f(i) is the time at which node i is finished.
+% pred(i) is the predecessor of i in the dfs tree.
+%
+% If the graph is a tree, preorder is parents before children,
+% and postorder is children before parents.
+% For a DAG, topological order = reverse(postorder).
+%
+% See Cormen, Leiserson and Rivest, "An intro. to algorithms" 1994, p478.
+
+n = length(adj_mat);
+
+global white gray black color
+white = 0; gray = 1; black = 2;
+color = white*ones(1,n);
+
+global time_stamp
+time_stamp = 0;
+
+global d f
+d = zeros(1,n);
+f = zeros(1,n);
+
+global pred
+pred = zeros(1,n);
+
+global cycle
+cycle = 0;
+
+global pre post
+pre = [];
+post = [];
+
+if ~isempty(start)
+  dfs_visit(start, adj_mat, directed);
+else
+  for u=1:n
+    if color(u)==white
+      dfs_visit(u, adj_mat, directed);
+    end
+  end
+end
+
+
+%%%%%%%%%%
+
+function dfs_visit(u, adj_mat, directed)
+
+global white gray black color time_stamp d f pred cycle  pre post
+
+pre = [pre u];
+color(u) = gray;
+time_stamp = time_stamp + 1;
+d(u) = time_stamp;
+if directed
+  ns = children(adj_mat, u);
+else
+  ns = neighbors(adj_mat, u);
+  ns = mysetdiff(ns, pred(u)); % don't go back to visit the guy who called you!
+end
+for v=ns(:)'
+  %fprintf('u=%d, v=%d, color(v)=%d\n', u, v, color(v))
+  switch color(v)
+    case white, % not visited v before (tree edge)
+     pred(v)=u;
+     dfs_visit(v, adj_mat, directed);
+   case gray, % back edge - v has been visited, but is still open
+    cycle = 1;
+    %fprintf('cycle: back edge from v=%d to u=%d\n', v, u);
+   case black, % v has been visited, but is closed
+    % no-op
+  end
+end
+color(u) = black;
+post = [post u];
+time_stamp = time_stamp + 1;
+f(u) = time_stamp;
+
+