Hack around an inconsistency between Rotation<3> and other target spaces,

notably the almost-equivalent UnitVector<4>: A vector with three entries
is interpreted by the UnitVector<4> class as a tangent vector given in
the basis returned by orthonormalFrame.  That is correct as it works
for all kinds of manifolds.  On the other hand, the Rotation<3> class
interprets as a 3x3 skew matrix (a tangent vector at the identity in
the matrix representation) even though the implementation used quaternion
coordinates.

To trick around this the use of exp methods with FieldVector<3> is avoided
by this patch.  A real fix would involve introducing a SkewMatrix class
and using that in Rotation<3>.

[[Imported from SVN: r7575]]

dune/gfe/riemanniantrsolver.cc

@@ -342,8 +342,17 @@ void RiemannianTrustRegionSolver<GridType,TargetSpace>::solve()
         // ////////////////////////////////////////////////////
         
         SolutionType newIterate = x_;
+#if 0   // out-commented until the Rotation class can distinguish skew-symmetric matrices from three-vectors
         for (int j=0; j<newIterate.size(); j++) 
             newIterate[j] = TargetSpace::exp(newIterate[j], corr[j]);
+#else
+        for (int j=0; j<newIterate.size(); j++) {
+            Dune::FieldMatrix<double,TargetSpace::TangentVector::size,TargetSpace::EmbeddedTangentVector::size> B = x_[j].orthonormalFrame();
+            Dune::FieldVector<double,TargetSpace::EmbeddedTangentVector::size> embeddedCorr(0);
+            B.mtv(corr[j], embeddedCorr);
+            newIterate[j] = TargetSpace::exp(newIterate[j], embeddedCorr);
+        }
+#endif
         
         double energy    = assembler_->computeEnergy(newIterate); 
         

dune/gfe/targetspacertrsolver.cc

@@ -107,7 +107,15 @@ void TargetSpaceRiemannianTRSolver<TargetSpace,N>::solve()
         // ////////////////////////////////////////////////////
         
         TargetSpace newIterate = x_;
+#if 0   // out-commented until the Rotation class can distinguish skew-symmetric matrices from three-vectors
         newIterate = TargetSpace::exp(newIterate, corr[0]);
+#else
+        Dune::FieldMatrix<double,TargetSpace::TangentVector::size,TargetSpace::EmbeddedTangentVector::size> B = x_.orthonormalFrame();
+        Dune::FieldVector<double,TargetSpace::EmbeddedTangentVector::size> embeddedCorr(0);
+        B.mtv(corr[0], embeddedCorr);
+   
+        newIterate = TargetSpace::exp(newIterate, embeddedCorr);
+#endif
         
         /** \todo Don't always recompute oldEnergy */
         double oldEnergy = assembler_->value(x_);