diff --git a/cpp/SubgraphPreconditioner-inl.h b/cpp/SubgraphPreconditioner-inl.h
index f3d42ed3b..cac25f24c 100644
--- a/cpp/SubgraphPreconditioner-inl.h
+++ b/cpp/SubgraphPreconditioner-inl.h
@@ -29,12 +29,20 @@ namespace gtsam {
 		list<Key> keys = predecessorMap2Keys(tree);
 
 		// split the graph
-		Key root = keys.back();
 		if (verbose_) cout << "generating spanning tree and split the graph ...";
 		G.template split<Key, Constraint>(tree, T_, C_);
 		if (verbose_) cout << T_.size() << " and " << C_.size() << " factors" << endl;
 
-		// theta_bar = composePoses<Graph, Constraint, Pose, Config> (T_, tree, config[root]);
+		// make the ordering
+		list<Symbol> symbols;
+		symbols.resize(keys.size());
+		std::transform(keys.begin(), keys.end(), symbols.begin(), key2symbol<Key>);
+		ordering_ = boost::shared_ptr<Ordering>(new Ordering(symbols));
+
+		// compose the approximate solution
+		Key root = keys.back();
+		theta_bar_ = composePoses<Graph, Constraint, Pose, Config> (T_, tree, config[root]);
+
 	}
 
 	/* ************************************************************************* */
@@ -43,7 +51,7 @@ namespace gtsam {
 			const Config& theta_bar, const Ordering& ordering) const {
 
 		VectorConfig zeros;
-		BOOST_FOREACH(const string& j, ordering) zeros.insert(j,zero(3));
+		BOOST_FOREACH(const Symbol& j, ordering) zeros.insert(j,zero(3));
 
 		// build the subgraph PCG system
 		GaussianFactorGraph Ab1 = T_.linearize(theta_bar);
diff --git a/cpp/SubgraphPreconditioner.h b/cpp/SubgraphPreconditioner.h
index b26fea3d2..6f5d1b7e6 100644
--- a/cpp/SubgraphPreconditioner.h
+++ b/cpp/SubgraphPreconditioner.h
@@ -9,6 +9,7 @@
 
 #include "GaussianFactorGraph.h"
 #include "GaussianBayesNet.h"
+#include "Ordering.h"
 
 namespace gtsam {
 
@@ -59,8 +60,6 @@ namespace gtsam {
 		void print(const std::string& s = "SubgraphPreconditioner") const;
 	};
 
-	class Ordering;
-
   /**
    * A linear system solver using subgraph preconditioning conjugate gradient
    */
@@ -76,12 +75,24 @@ namespace gtsam {
 		const bool verbose_;
 		const double epsilon_, epsilon_abs_;
 
+		/* the ordering derived from the spanning tree */
+		boost::shared_ptr<Ordering> ordering_;
+
+		/* the solution computed from the first subgraph */
+		boost::shared_ptr<Config> theta_bar_;
+
 		NonlinearGraph T_, C_;
 
 	public:
-		SubgraphPCG() {}
+		// kai: this constructor is for compatible with Factorization
+		SubgraphPCG() { throw std::runtime_error("SubgraphPCG: this constructor is only for compatibility!");}
+
 		SubgraphPCG(const NonlinearGraph& G, const Config& config);
 
+		boost::shared_ptr<Ordering> ordering() const { return ordering_; }
+
+		boost::shared_ptr<Config> theta_bar() const { return theta_bar_; }
+
   	/**
   	 * solve for the optimal displacement in the tangent space, and then solve
   	 * the resulted linear system