diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h
index f60ef1c..9b67dd5 100644
--- a/Eigen/src/Core/SolveTriangular.h
+++ b/Eigen/src/Core/SolveTriangular.h
@@ -49,7 +49,7 @@
   {
     static const int PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
     ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
-    
+
     const int size = lhs.cols();
     for(int pi=IsLowerTriangular ? 0 : size;
         IsLowerTriangular ? pi<size : pi>0;
@@ -224,7 +224,7 @@
   ei_assert(!(Mode & ZeroDiagBit));
   ei_assert(Mode & (UpperTriangularBit|LowerTriangularBit));
 
-  enum { copy = ei_traits<RhsDerived>::Flags & RowMajorBit };
+  enum { copy = ei_traits<RhsDerived>::Flags & RowMajorBit  && RhsDerived::IsVectorAtCompileTime };
   typedef typename ei_meta_if<copy,
     typename ei_plain_matrix_type_column_major<RhsDerived>::type, RhsDerived&>::ret RhsCopy;
   RhsCopy rhsCopy(rhs);
diff --git a/Eigen/src/Core/products/TriangularSolverMatrix.h b/Eigen/src/Core/products/TriangularSolverMatrix.h
index 7842f87..e49fac9 100644
--- a/Eigen/src/Core/products/TriangularSolverMatrix.h
+++ b/Eigen/src/Core/products/TriangularSolverMatrix.h
@@ -25,7 +25,7 @@
 #ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_H
 #define EIGEN_TRIANGULAR_SOLVER_MATRIX_H
 
-// if the rhs is row major, we have to evaluate it in a temporary colmajor matrix
+// if the rhs is row major, let's transpose the product
 template <typename Scalar, int Side, int Mode, bool Conjugate, int TriStorageOrder>
 struct ei_triangular_solve_matrix<Scalar,Side,Mode,Conjugate,TriStorageOrder,RowMajor>
 {
@@ -34,22 +34,16 @@
     const Scalar*  tri, int triStride,
     Scalar* _other, int otherStride)
   {
-    
     ei_triangular_solve_matrix<
       Scalar, Side==OnTheLeft?OnTheRight:OnTheLeft,
-      (Mode&UnitDiagBit) | (Mode&UpperTriangular) ? LowerTriangular : UpperTriangular,
-      !Conjugate, TriStorageOrder, ColMajor>
+      (Mode&UnitDiagBit) | ((Mode&UpperTriangular) ? LowerTriangular : UpperTriangular),
+      NumTraits<Scalar>::IsComplex && Conjugate,
+      TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor>
       ::run(size, cols, tri, triStride, _other, otherStride);
-
-//     Map<Matrix<Scalar,Dynamic,Dynamic> > other(_other, otherStride, cols);
-//     Matrix<Scalar,Dynamic,Dynamic> aux = other.block(0,0,size,cols);
-//     ei_triangular_solve_matrix<Scalar,Side,Mode,Conjugate,TriStorageOrder,ColMajor>
-//       ::run(size, cols, tri, triStride, aux.data(), aux.stride());
-//     other.block(0,0,size,cols) = aux;
   }
 };
 
-/* Optimized triangular solver with multiple right hand side (_TRSM)
+/* Optimized triangular solver with multiple right hand side and the triangular matrix on the left
  */
 template <typename Scalar, int Mode, bool Conjugate, int TriStorageOrder>
 struct ei_triangular_solve_matrix<Scalar,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>
@@ -190,11 +184,8 @@
     Scalar* _other, int otherStride)
   {
     int rows = otherSize;
-//     ei_const_blas_data_mapper<Scalar, TriStorageOrder> rhs(_tri,triStride);
-//     ei_blas_data_mapper<Scalar, ColMajor> lhs(_other,otherStride);
-
-    Map<Matrix<Scalar,Dynamic,Dynamic,TriStorageOrder> > rhs(_tri,size,size);
-    Map<Matrix<Scalar,Dynamic,Dynamic,ColMajor> > lhs(_other,rows,size);
+    ei_const_blas_data_mapper<Scalar, TriStorageOrder> rhs(_tri,triStride);
+    ei_blas_data_mapper<Scalar, ColMajor> lhs(_other,otherStride);
 
     typedef ei_product_blocking_traits<Scalar> Blocking;
     enum {
@@ -203,8 +194,8 @@
       IsLowerTriangular = (Mode&LowerTriangular) == LowerTriangular
     };
 
-    int kc = std::min<int>(/*Blocking::Max_kc/4*/32,size); // cache block size along the K direction
-    int mc = std::min<int>(/*Blocking::Max_mc*/32,size);   // cache block size along the M direction
+    int kc = std::min<int>(Blocking::Max_kc/4,size); // cache block size along the K direction
+    int mc = std::min<int>(Blocking::Max_mc,size);   // cache block size along the M direction
 
     Scalar* blockA = ei_aligned_stack_new(Scalar, kc*mc);
     Scalar* blockB = ei_aligned_stack_new(Scalar, kc*size*Blocking::PacketSize);
@@ -214,7 +205,6 @@
     ei_gemm_pack_rhs<Scalar,Blocking::nr,RhsStorageOrder> pack_rhs;
     ei_gemm_pack_rhs<Scalar,Blocking::nr,RhsStorageOrder,true> pack_rhs_panel;
     ei_gemm_pack_lhs<Scalar, Blocking::mr, ColMajor, false, true> pack_lhs_panel;
-    ei_gemm_pack_lhs<Scalar, Blocking::mr, ColMajor, false> pack_lhs;
 
     for(int k2=IsLowerTriangular ? size : 0;
         IsLowerTriangular ? k2>0 : k2<size;
@@ -224,7 +214,7 @@
       int actual_k2 = IsLowerTriangular ? k2-actual_kc : k2 ;
 
       int startPanel = IsLowerTriangular ? 0 : k2+actual_kc;
-      int rs = IsLowerTriangular ? actual_k2 : size - actual_k2 - actual_kc;        
+      int rs = IsLowerTriangular ? actual_k2 : size - actual_k2 - actual_kc;
       Scalar* geb = blockB+actual_kc*actual_kc*Blocking::PacketSize;
 
       if (rs>0) pack_rhs(geb, &rhs(actual_k2,startPanel), triStride, -1, actual_kc, rs);
@@ -239,8 +229,6 @@
           int panelOffset = IsLowerTriangular ? j2+actualPanelWidth : 0;
           int panelLength = IsLowerTriangular ? actual_kc-j2-actualPanelWidth : j2;
 
-//           std::cerr << "$ " << k2 << " " << j2 << " " << actual_j2 << " " << panelOffset << " " << panelLength << "\n";
-
           if (panelLength>0)
           pack_rhs_panel(blockB+j2*actual_kc*Blocking::PacketSize,
                          &rhs(actual_k2+panelOffset, actual_j2), triStride, -1,
@@ -269,7 +257,6 @@
             int panelLength = IsLowerTriangular ? actual_kc - j2 - actualPanelWidth : j2;
 
             // GEBP
-            //if (lengthTarget>0)
             if(panelLength>0)
             {
               gebp_kernel(&lhs(i2,absolute_j2), otherStride,
@@ -284,18 +271,17 @@
             {
               int j = IsLowerTriangular ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k;
 
-              Scalar a = (Mode & UnitDiagBit) ? Scalar(1) : Scalar(1)/conj(rhs(j,j));
-              for (int i=0; i<actual_mc; ++i)
+              Scalar* r = &lhs(i2,j);
+              for (int k3=0; k3<k; ++k3)
               {
-                int absolute_i = i2+i;
-                Scalar b = 0;
-                for (int k3=0; k3<k; ++k3)
-                  if(IsLowerTriangular)
-                    b += lhs(absolute_i,j+1+k3) * conj(rhs(j+1+k3,j));
-                  else
-                    b += lhs(absolute_i,absolute_j2+k3) * conj(rhs(absolute_j2+k3,j));
-                lhs(absolute_i,j) = (lhs(absolute_i,j) - b)*a;
+                Scalar b = conj(rhs(IsLowerTriangular ? j+1+k3 : absolute_j2+k3,j));
+                Scalar* a = &lhs(i2,IsLowerTriangular ? j+1+k3 : absolute_j2+k3);
+                for (int i=0; i<actual_mc; ++i)
+                  r[i] -= a[i] * b;
               }
+              Scalar b = (Mode & UnitDiagBit) ? Scalar(1) : Scalar(1)/conj(rhs(j,j));
+              for (int i=0; i<actual_mc; ++i)
+                r[i] *= b;
             }
 
             // pack the just computed part of lhs to A
@@ -304,7 +290,7 @@
                            actual_kc, j2);
           }
         }
-        
+
         if (rs>0)
           gebp_kernel(_other+i2+startPanel*otherStride, otherStride, blockA, geb,
                       actual_mc, actual_kc, rs);